Program

Standard Talks, Mornings

Working Sessions, Afternoons (15:00-18:00)


23/1 - Monday 24/1 - Tuesday 25/1 - Wednesday

 8:30-8:50 

Opening ceremony

8:50-9:00

  

                      Aaron Siegel,                                           Twitter, Inc,                      TBA



    

9:00-9:20

 

Milos Stojakovic,
University of Novi Sad,
 Strong avoiding positional games 

                                 Dana Ernst,                                                    Northern Arizona University,                                  Impartial geodetic convexity achievement                     and avoidance games on graphs   

 

 9:20-9:40         

 

Alda Carvalho,
          ISEL-IPL & CEMAPRE/REM-UL,                     «All is number»? Not so easy,                               Mr. Pythagoras                                              

Danijela Popović,
Mathematical Institute of SASA,
         A new approach to equivalence of                                     games                                

Neil McKay,
University of New Brunswick,
Numbers and ordinal sums

 

  

9:40-10:00

          

  

TBA,

     

  

     

Michael Fisher,
West Chester University,
 Olympic games: three impartial   games with infinite octal codes


Paul Ellis,
Manhattanville College,
                      The arithmetic-periodicity                                                of Cut for C = {1, 2c}                           

       

 

10:00-10:20                                    

   

  

Koki Suetsugu,
National Institute of Informatics,
    Some new universal partizan rulesets 

   

Richard J. Nowakowski,
Dalhousie University,
 The game of Flipping Coins

   

  

Craig Tennenhouse,
University of New England,
 Vexing vexillological logic

  

   

10:20-10:40


             Carlos Pereira dos Santos,                        CMA (NovaMath), FCT NOVA,             Disjunctive sums of quasi-nimbers

                                                                  Tomoaki Abuku,
National Institute of Informatics,
A Multiple Hook Removing Game whose starting position is a rectangular Young diagram with unimodal numbering 

 

                                                                                                        Mirjana Mikalačk,                        University of Novi Sad,
  Multistage positional games

 

10:40-11:10

  

 
Coffee-break

 
Coffee-break

 
Coffee-break

  

11:10-11:30

 

Bernhard von Stengel,
London School of Economics,
Zero-sum games and linear programming duality 

                         Kyle Burke,                                          Plymouth State University,                 Divine Nimtervention

                           Nandor Sieben,                                                 Northern Arizona University,                   Impartial hypergraph games

   

11:30-11:50

Bojan Bašić,
University of Novi Sad,
A twist on the classical
prisoners-in-a-line hat-guessing game

                    Kanae Yoshiwatari,                                   Nagoya University,                Complexity of Colored Arc Kayles

                            Svenja Huntemann,                                                     Concordia University,                          Temperature of Partizan ArcKayles Trees

  

11:50-12:10


                       Hironori Kiya,                                          Kyushu University,                      Normal-play with dead-end-winning convention



                                                                                       Eric Duchêne,                                        LIRIS, Lyon 1 University,                 Partizan subtraction games 

                                             

Florian Galliot,
University of Grenoble Alpes,
    The Maker-Breaker game on hypergraphs of rank 3:         structural results and a polynomial-time algorithm                                                 

  

12:10-12:30

Silvia Heubach,
California State University,
    On the Structure of the P-positions
of Slow Exact k-Nim

Aline Parreau,
CNRS, Lyon 1 University,
    Maker-Breaker Domination Game

 Prem Kant,
Indian Institute of Technology Bombay,
   Bidding combinatorial games 

  

12:30-12:50

Keito Tanemura,
Kwansei Gakuin University,
    Chocolate games with a pass and 
an application of symbolic regression to these games

TBA

    

 Nacim Oijid,
University of Lyon,
   Bipartite instances of Influence

  

12:50-13:20

TBA
 
  
 

Hikaru Manabe,
       Keimei Gakuen Elementary Junior &         Senior High School,
    Four-dimensional chocolate games and      chocolate games with a pass move

 TBA
  
     

   

13:20-15:00                     

 
Break for lunch

 
Break for lunch

 
Break for lunch

   

15:00-18:00                     

 
Working sessions

 
Working sessions

 
Working sessions

   

19:00-23:00                      

Conference Dinner



Alda Carvalho, ISEL-IPL&CEMAPRE/REM-University of Lisbon, Portugal

Title: 
«All is number»? Not so easy, Mr. Pythagoras

Abstract: We present a method to evaluate if a ruleset only has positions whose game values are numbers.

(Joint work with Melissa Huggan, Richard J. Nowakowski, and Carlos Pereira dos Santos)

  

Aline Parreau, CNRS, Lyon 1 University, France

Title: Maker-Breaker Domination Game

Abstract: The Maker-Breaker Domination Game is played on a graph G with two players Dominator and Staller. At his turn, Dominator, selects a vertex in order to dominate the graph while at his turn Staller forbids a vertex to Dominator in order to prevent him to reach his goal. Both players play alternately without missing their turn.  We study the problem of deciding who has a winning strategy for a given graph G. We prove that this problem is PSPACE-complete, even for bipartite graphs and split graphs but is polynomial for cographs, trees and block graphs. We in particular focus on pairing strategies for Dominator and prove that having a pairing strategy is the only way to win in cographs, trees, block graphs and interval graphs.

(Joint work with Guillaume Bagan, Eric Duchêne, Valentin Gledel, Tuomo Lehtilä, and Gabriel Renault)

      

Bernhard von Stengel, London School of Economics, United Kingdom

Title: 
Zero-sum games and linear programming duality

Abstract: The minimax theorem for zero-sum games is easily proved from the strong duality theorem of linear programming. For the converse direction, the standard proof by Dantzig (1951) is massively incomplete, as we argue in this article. We explain and combine classical theorems about solving linear equations with nonnegative variables to give a correct alternative proof.

    

Bojan Bašić, University of Novi Sad, Serbia

Title: 
A twist on the classical prisoners-in-a-line hat-guessing game

Abstract: The game in which a warden arranges n prisoners in a line and then each of them guesses (one by one) whether the hat on his head is white or black, aiming to maximize the total number of correct guesses, is a folklore thing. Those who hear it for the first time (though today it is not easy to meet such a person) are usually surprised when they learn that (spoiler alert!) all the prisoners with the exception of only one can secure correct guesses. And furthermore, nothing changes if the hats come in more than two colors: in that case, too, one prisoner can single-handedly transmit enough information so that all the other prisoners be able to deduce their hat colors. They simply establish a bijection between the available hat colors and a complete residue system modulo the number of colors, and then the first prisoners declares the sum of hats of all the other prisoners (under the same modulus). This is one of many puzzles in circulation featuring prisoners and a warden. And although they are formulated in an informal fashion and often presented as a matter of recreational mathematics, many of them hide serious science under their facade. There are tight connections between these puzzles and game theory, information theory, coding theory etc. In this talk we introduce a variant of this game, where information that prisoners can relay to other prisoners is much more restricted. In particular, each prisoner is asked whether he wants to take a guess on his hat color, to which question he answers aloud (everybody hears that); if the answer is affirmative, he takes a guess but the other prisoners do not hear what his guess is, they only get to know whether the guess was correct. Therefore, basically, each prisoner is able to transmit only a single binary bit («yes»/«no» answer), and although the other prisoners do get a little more information (the outcome of the guess), the prisoner who takes a guess cannot directly control this further affair. Clearly, if there are 4 possible colors, the first two prisoners can encode the sum of colors of all the remaining prisoners, and thus all but the first two prisoners can assure correct guesses. What is, however, perhaps somewhat surprising, and which will be the first case seen in the talk, is that, if there are 5 hat colors, the prisoners still can arrange a strategy that will guarantee correct guesses for all of them but the first two (and 5 is the largest such number). We shall then present some results on the general question what the maximal possible number of colors is such that, given a positive integer m, if n prisoners are playing the game with the indicated number of colors, they can devise a strategy such that all but m prisoners are guaranteed to guess correctly.

(Joint work with Vlado Uljarević)

    

Carlos Pereira dos Santos, Center for Mathematics and Applications (NovaMath), FCT NOVA, Portugal

Title: Disjunctive sums of quasi-nimbers

Abstract: Paint can is an example of a game whose positions are disjunctive sums, and a move in any component reduces that component to a nimber. Conway, in On Numbers and Games, partially analysed the related game Supernim, and called these components «superstars», mentioning «There does not appear to be a complete theory». The book contains one result about these games, and, until now, there has been no advance in finding good strategies. Here, we show that, for a human, the use of canonical forms is not a good approach. We present an algorithmic, recursive approach to the general case, based on a fundamental reduction of these positions, as well as on a Nimber Avoidance Theorem.

(Joint work with Alexandre Silva, João Pedro Neto, and Richard J. Nowakowski)

   

Craig Tennenhouse, University of New England, United States of America

Title: Vexing vexillological logic

Abstract: We define a new impartial combinatorial game, Flag Coloring, based on flood filling. We then generalize to a graph game and demonstrate that the generalized game is PSPACE-complete for two colors or more via a reduction from the game Avoid True, determine the outcome classes of games based on real-world flags, and discuss remaining open problems.

(Joint work with Kyle Burke)

   

Dana Ernst, Northern Arizona University, United States of America

Title: Impartial geodetic convexity achievement and avoidance games on graphs

Abstract: A set P of vertices of a graph G is convex if it contains all vertices along shortest paths between vertices in P. The convex hull of P is the smallest convex set containing P. We say that a subset of vertices P generates the graph G if the convex hull of P is the entire vertex set.  We study two impartial games Generate and Do Not Generate in which two players alternately take turns selecting previously-unselected vertices of a finite graph G. The first player who builds a generating set for the graph from the jointly-selected elements wins the achievement game GEN(G). The first player who cannot select a vertex without building a generating set loses the avoidance game DNG(G). Similar games have been considered by several authors, including Harary et al. In this talk, we determine the nim-number for several graph families, including trees, cycle graphs, complete graphs, complete bipartite graphs, and hypercube graphs.

(Joint work with Bret Benesh, Marie Meyer, Sarah Salmon, and Nandor Sieben)

         

Danijela Popović, Mathematical Institute of SASA, Serbia

Title: A new approach to equivalence of games

Abstract: The well-known Sprague-Grundy theory states that every impartial combinatorial game played under the so-called normal play convention is equivalent to a single Nim heap. However, this theory does not tell anything about the structure of game graphs of the concerned games, and does not work under the misère play convention. We suggest a new notion of equivalence of games, named emulational equivalence. It is stronger than the Sprague-Grundy equivalence and weaker than the isomorphism of game graphs, and it can be applied regardless of whether the game is played under normal or under misère convention. Additionally, we introduce a new game on graphs named Hackenforb, which turns out to have a great emulational potential, namely, for various impartial games we were able to construct Hackenforb instances emulationally equivalent to them.

(Joint work with Bojan Bašić and Nikola Milosavljević)

   

Eric Duchêne, LIRIS, Lyon 1 University, France

Title: Partizan subtraction games

Abstract: Partizan subtraction games are combinatorial games where two players, Left and Right, alternately remove a number n of tokens from a heap of tokens, with nSL (resp. nSR) when it is Left's (resp. Right's) turn. The first player unable to move loses. These games were introduced by Fraenkel and Kotzig in 1987, where they introduced the notion of dominance, i.e. an asymptotic behavior of the outcome sequence where Left always wins if the heap is sufficiently large. In the current work, we investigate the other kinds of behaviors for the outcome sequence. In addition to dominance, three other disjoint behaviors are defined, namely weak dominance, fairness and ultimate impartiality. We consider the problem of computing this behavior with respect to SL and SR, which is connected to the well-known Frobenius coin problem. General results are given, together with arithmetic and geometric characterizations when the sets SL and SR have size at most 2.

(Joint work with Marc Heinrich, Richard J. Nowakowski, and Aline Parreau)

      

Florian Galliot, University of Grenoble Alpes, France

Title: The Maker-Breaker game on hypergraphs of rank 3: structural results and a polynomial-time algorithm

Abstract: In the Maker-Breaker positional game, Maker and Breaker take turns by picking vertices from a hypergraph H, and Maker wins if and only if he claims all the vertices of some edge of H. We introduce a general notion of danger at a vertex x, which is a subhypergraph representing an urgent threat that Breaker must hit with his next pick if Maker picks x. Applying this concept in hypergraphs of rank 3, we get a structural characterization of the winner with perfect play as well as optimal strategies for both players based on danger intersections. More specifically: we construct a family F of dangers such that a hypergraph H of rank 3 is a Breaker win if and only if the F-dangers at x in H intersect for all x. By construction of F, this will mean that H is a Maker win if and only if Maker can guarantee the appearance, within the first three rounds of play, of a specific elementary subhypergraph (on which Maker easily wins) consisting of a linear path or cycle. This last result has a consequence on the algorithmic complexity of deciding which player has a winning strategy on a given hypergraph: this problem, which has been shown by Rahman and Watson to be PSPACE-complete on 6-uniform hypergraphs, is in polynomial time on hypergraphs of rank 3. This validates a conjecture by Rahman and Watson. Another corollary of our result is that, if Maker has a winning strategy on a hypergraph of rank 3, then he can ensure to claim an edge in a number of rounds that is logarithmic in the number of vertices.

(Joint work with Sylvain Gravier and Isabelle Sivignon)

   

Hikaru Manabe, Keimei Gakuen Elementary Junior & Senior High School, Japan

Title:
Four-dimensional chocolate games and chocolate games with a pass move

Abstract: The authors have studied three-dimensional chocolate bar games that are variants of game of Nim, and they will generalize them to the case of four-dimensional chocolate bar games. They presented the necessary and sufficient condition whereby a three-dimensional chocolate bar may have a Grundy number (p-1) xor (q-1) xor (r-1), where pq, and are the length, height, and width of the bar in 2021. In this talk, they will present a four-dimensional version of the theorem and use it for the three-pile nim with a pass move. Here, we modify the game's standard rules to allow a one-time pass, that is, a pass move that may be used at most once in the game and not from a terminal position. Once either player has used a pass, it is no longer available. It is well-known that in classical Nim, the introduction of the pass alters the underlying structure of the game, significantly increasing its complexity. Using the fourth-dimensional coordinate for the pass move, we can treat a three-pile nim with a pass move as a four-dimensional chocolate bar game. This approach opens a new perspective on the complexity of the traditional three-pile with a pass.

(Joint work with Aditi Singh, Yuki Tokuni, and Ryohei Miyadera)

       

Hironori Kiya, Kyushu University, Japan

Title: 
Normal-play with dead-end-winning convention

Abstract: We consider a new winning convention of partizan games. The loser of a game under this convention is the player who cannot play anymore except for the case that the position is dead for the player, that is, the player can no longer make moves; In this case, they win. A famous game under this convention is Shichinarabe, which is similar to card Dominoes, sevens, Fan Tan, and Showdown. We characterize the game such that in each turn the number of options is at most one.

(Joint work with Koki Suetsugu)

   

Kanae Yoshiwatari, Nagoya University, Japan

Title: 
Complexity of Colored Arc Kayles

Abstract: Cram, Domineering, and Arc Kayles are well-studied combinatorial games that can be interpreted as edge-selecting-type games on graphs. In this talk, we introduce a generalization, called Colored Arc Kayles (which includes these games), discussing its complexity.

(Joint work with Tesshu Hanaka, Hironori Kiya, and Hirotaka Ono)

   

Keito Tanemura, Kwansei Gakuin University, Japan


Title: 
Chocolate games with a pass and an application of symbolic regression to these games

Abstract: The authors present their research on several combinatorial games with a pass move, and the application of symbolic regression to these games. These games are chocolate games, Moore's Nim, and Restricted Nim. Here, the game's standard rules are modified to allow a one-time pass, that is, a pass move that may be used at most once in the game and not from a terminal position. Once either player has used a pass, it is no longer available. It is well-known that in classical three-pile Nim, the introduction of the pass alters the underlying structure of the game, significantly increasing its complexity, but in chocolate games, Moore's Nim and Restricted Nim the pass move was found to have a minimal impact. There is a simple formula for the previous player's position for these games. In chocolate games and Restricted Nim, there are also simple formulas for the cases in that Grundy numbers are 1,2,3, …. When the authors studied the previous player's positions and formulas for Grundy numbers, they used a symbolic regression library that the authors made. Each formula is different for each Grundy number, and discovering the formula is a time-consuming task for human beings. Therefore, symbolic regression is a valuable tool in the research of combinatorial games. The authors present the basic structure of their software in this article.

(Joint work with Yuji Sasaki, Hikaru Manabe, Yuki Tokuni, and Ryohei Miyadera )

     

Koki Suetsugu, National Institute of Informatics, Japan

Title: 
Some new universal partizan rulesets

Abstract: A universal partizan ruleset is a ruleset in which every finite value can appear as a position. Generalized Konane is the only ruleset which has been proven as a universal partizan ruleset. In this talk, we introduce three new partizan univesal rulesets. One is proved by a constructive method. The others are proved by reduction. Reduction is often used for proofs of complexity (like PSPACE-Complete or NP-Complete). In this talk, we show that it can also be used for proving that a ruleset is a universal partizan ruleset. 

     

Kyle Burke, Plymouth State University, United States of America

Title: 
Divine Nimtervention

Abstract: What if, while playing Nim, the entities sitting on our shoulders intercepted and modified the positions in an attempt to help or hinder us in the match.  For example, if a player has an angel on their shoulder, after their turn, it will check that the resulting position has a nim sum of zero.  If it doesn't, it will make an "extra move" to reach a zero-position.  Demons, on the other hand, will do the opposite, shooting for a non-zero sum.  In this talk, we consider the different combinations of angels and demons and look at the properties of the rulesets that arise. 

(Joint work with Craig Tennenhouse)

       

Michael Fisher, West Chester University, United States of America

Title: 
Olympic games: three impartial games with infinite octal codes

Abstract: In this talk we will look at three subtraction games, each describable using an infinite octal code.  The P-positions will be enumerated.  Additionally, we will see why knowing the complete Grundy function is likely out of reach.

   

Milos Stojakovic, University of Novi Sad, Serbia

Title: 
Strong avoiding positional games

Abstract: Given an increasing graph property F, the strong Avoider-Avoider F game is played on the edge set of a complete graph. Two players, Red and Blue, take turns in claiming previously unclaimed edges with Red going first, and the player whose graph possesses F first loses the game. If the property F is «containing a fixed graph H», we refer to the game as the H game. We show that Blue has a winning strategy in two strong Avoider-Avoider games, P4 game and CC>3 game, where CC>3 is the property of having at least one connected component on more than three vertices. These are some of the first non-trivial Avoider-Avoider games for which the outcome is determined. We also study a variant, the strong CAvoider-CAvoider games, with the additional requirement that the graph of each of the players must stay connected throughout the game. We prove that Blue has a winning strategy in several trong CAvoider-CAvoider games. 

(Joint work with Jelena Stratijev)

   

Mirjana Mikalački, University of Novi Sad, Serbia

Title: 
Multistage positional games

Abstract: We initiate the study of a new variant of the Maker-Breaker positional game, which we call multistage game. Given a hypergraph of the game H, and the bias b, the (1:b) multistage Maker-Breaker game is played in several stages as follows. Each stage is played as a usual (1:b) Maker-Breaker game, until all the elements of the board get claimed by one of the players, with the first stage being played on H. In every subsequent stage, the game is played on the board reduced to the elements that Maker claimed in the previous stage, and with the winning sets reduced to those fully contained in the new board. The game proceeds until no winning sets remain, and the goal of Maker is to prolong the duration of the game for as many stages as possible. In this paper we estimate the maximum duration of the (1:b) multistage Maker-Breaker game, for biases b subpolynomial in n, for some standard graph games played on the edge set of Kn the connectivity game, the Hamilton cycle game, the non-k-colorability game, the pancyclicity game and the H-game. While the first three games exhibit a probabilistic intuition, it turns out that the last two games fail to do so.

(Joint work with Juri Barkey, Dennis Clemens, Fabian Hamann, and Amedeo Sgueglia)

    

Nacim Oijid, University of Lyon, France

Title: 
Bipartite instances of Influence

Abstract: The game Influence is a scoring combinatorial game that has been introduced in 2021 by Duchene et al. It is a good representative of Milnor's universe of scoring games, i.e. games where it is never interesting for a player to miss his turn. New general results are first given for this universe, by transposing the notions of mean and temperature derived from non-scoring combinatorial games. Such results are then applied to Influence to refine the case of unions of paths started in the previous paper. The computational complexity of the score of the game is also solved and proved to be PSPACE-complete. We finally focus on some specific cases of Influence when the graph is bipartite, by giving explicit strategies and bounds on the optimal score on structures like grids, hypercubes or tori.   

   

Nandor Sieben, Northern Arizona University, United States of America

Title: 
Impartial hypergraph games

Abstract: We study two building games and two removing games played on a finite hypergraph. In each game two players take turns selecting vertices of the hypergraph until the set of jointly selected vertices satisfies a condition related to the edges of the hypergraph. The winner is the last player able to move. The building achievement game ends as soon as the set of selected vertices contains an edge. In the building avoidance game the players are not allowed to select a set that contains an edge. The removing achievement game ends as soon as the complement of the set of selected vertices no longer contains an edge. In the removing avoidance game the players are not allowed to select a set whose complement does not contain an edge. We develop some generic tools for finding the nim-value of these games and show that the nim-value can be an arbitrary nonnegative integer. The outcome of many of these games were previously determined for several special cases in algebraic and combinatorial settings. We provide several examples and show how our tools can be used to refine these results by finding nim-values.

   

Neil McKay, University of New Brunswick, Canada

Title: 
Numbers and ordinal sums

Abstract: There are many rulesets in which all values are numbers and yet the values are difficult to compute. Blue-Red Hackebush stalk values are easy to compute as the positions are ordinal sums of numbers in canonical form. Recently some rulesets have had positions described using ordinal sums but as the summands are not in canonical form the values are hard to understand and compute. We explore forms of numbers for which values are easy to compute and a ruleset, Teetering Towers, where we can effectively compute values.

   

Paul Ellis, Manhattanville College, United States of America

Title: 
The arithmetic-periodicity of Cut for = {1, 2c}

Abstract: Cut is a class of partition games played on a finite number of finite piles of tokens. Each version of Cut is specified by a cut-set C ⊆ N. A legal move consists of selecting one of the piles and partitioning it into d + 1 nonempty piles, where d ∈ C. No tokens are removed from the game. It turns out that the nim-set for any C = {1, 2c} with c ≥ 2 is arithmetic-periodic, which answers an open question of Dailly et al. (Discrete Applied Mathematics, 285, 2020). The key step is to show that there is a correspondence between the nim-sets of Cut for C = {1, 6} and the nim-sets of Cut for C = {1, 2c}, c ≥ 4. The result easily extends to the case of C = {1, 2c1 2c22c3, ...}, where c1c2c3,... ≥ 2.

(Joint work with Thotsaporn Aek Thanitapinonda)

   

Prem Kant, Indian Institute of Technology Bombay, India

Title: 
Bidding combinatorial games

Abstract: We generalize the alternating play convention in normal play combinatorial games by means of Discrete Richman Auctions (Develin et al. 2010, Larsson et al. 2021, Lazarus et al. 1996). Under this framework, for infinitely many monoids of short games, we propose algorithmic play solutions to compare games. We then establish various general results such as group structures of integers and dyadic rationals, a simplicity theorem and existence of infinitesimals.

(Joint work with Urban Larsson, Ravi K. Rai, and Akshay V. Upasany)

      

 

Richard J. Nowakowski, Dalhousie University, Canada

Title: 
The game of Flipping Coins

Abstract: We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers (there is a link to Alda Carvalho' talk), and these are found by first applying a reduction, then decomposing the position into an iterated ordinal sum. This is unusual since moves in the middle of the line do not eliminate the rest of the line. Moreover, when G is decomposed into lines H and K, then G = H:R, where are the right options of K. This is in contrast to Hackenbush Strings where G = H:K.

(Joint work with Anthony Bonato and Melissa Huggan)

     

Silvia Heubach, California State University, United States of America

Title:
O
n the Structure of the P-positions of Slow Exact k-Nim

Abstract: Slow Exact k-Nim is a variant of the well-known game of  Nim. The rules of this variant are that in each move, of the n stacks are selected and then one token is removed from each of the k stacks.  The last player to move wins.  We prove results on the structure of the P-positions for the infinite family of games where we play on all but one of the n stacks.

(Joint work with Matthieu Dufour)

   

Svenja Huntemann, Concordia University, Canada

Title: 
Temperature of Partizan ArcKayles Trees

Abstract: Partizan ArcKayles (PArcK) is a generalization of both ArcKayles and Domineering. It is played on any finite, simple graph in which the edges are coloured red or blue. The players take turns removing an edge of their colour, including the two incident vertices, until the active player has no possible moves. Motivated by the conjecture that the temperature of Domineering is at most 2, we are studying the temperature of PArcK, concentrating on trees to begin with.

(Joint work with Neil McKay)

   

Tomoaki Abuku, National Institute of Informatics, Japan

Title: 
A Multiple Hook Removing Game whose starting position is a rectangular Young diagram with unimodal numbering

Abstract: We introduce a new impartial game named Multiple Hook Removing Game (MHRG for short). We also determine the G-values of some game positions (including the starting positions) in MHRG(m,n), the MHRG whose starting position is the rectangular Young diagram of size n with the unimodal numbering. In addition, we prove that MHRG(m,n) is isomorphic, as games, to MHRG(m,n+1) (if ≤ n and m+n is even), and give a relationship between MHRG(n,n+1) (and MHRG(n,n)) and HRG(Sn), the Hook Removing Game in terms of shifted Young diagrams.

(Joint work with Masato Tada)

   

List of Participants: 

Aaron Siegel, Twitter, Inc, United States of America 

Adam Atkinson, Ericsson, United Kingdom

Alda Carvalho, ISEL-IPL&CEMAPRE/REM-University of Lisbon, Portugal

Aline Parreau, CNRS, Lyon 1 University, France

Ana Paula Garrão, University of Azores, Portugal

Annamaria Cucinotta, Italy

Antoine Dailly, Laboratory of Informatics, Modelling and Optimization of the Systems, France

Bernhard von Stengel, London School of Economics, United Kingdom

Bojan BašićUniversity of Novi Sad, Serbia

Carlos Pereira dos Santos, Center for Mathematics and Applications (NovaMath), FCT NOVA, Portugal

Craig Tennenhouse, University of New England, United States of America

Dana Ernst, Northern Arizona University, United States of America

Danijela Popović, Mathematical Institute of SASA, Serbia

David Wolfe, Verisk, Canada

Eric Duchêne, LIRIS, Lyon 1 University, France

Florian Galliot, University of Grenoble Alpes, France

Hikaru Manabe, Keimei Gakuen Elementary Junior & Senior High School, Japan

Hironori Kiya, Kyushu University, Japan

Hirotaka Ono, Nagoya University, Japan

Jeanette Shakalli, FUNDAPROMAT, Panama

Kanae Yoshiwatari, Nagoya University, Japan

Keito Tanemura, Kwansei Gakuin University, Japan

Koki Suetsugu, National Institute of Informatics, Japan

Kyle Burke, Plymouth State University, United States of America

Margarida Raposo, University of Azores, Portugal

Matthieu Dufour, University of Quebec, Canada

Michael Fisher, West Chester University, United States of America

Milica MaksimovićUniversity of Novi Sad, Serbia

Milos Stojakovic, University of Novi Sad, Serbia

Mirjana Mikalački, University of Novi Sad, Serbia

Nacim Oijid, University of Lyon, France

Nandor Sieben, Northern Arizona University, United States of America

Neil McKay, University of New Brunswick, Canada

Paul Ellis, Manhattanville College, United States of America

Prem Kant, Indian Institute of Technology Bombay, India

Ricardo Teixeira, University of Azores, Portugal

Richard J. Nowakowski, Dalhousie University, Canada

Ryan Hayward, University of Alberta, Canada

Silvia Heubach, California State University, United States of America

Svenja Huntemann, Concordia University, Canada

Thotsaporn Aek Thanitapinonda, Mahidol University, United States of America

Tiago Hirth, University of Lisbon, Portugal

Tomoaki Abuku, National Institute of Informatics, Japan

Urban Larsson, Indian Institute of Technology Bombay, India