We consider the two-player game chomp on posets associated to numerical semigroups and show that the analysis of strategies for chomp is strongly related to classical properties of semigroups. We characterize which player has a winning-strategy for symmetric semigroups, semigroups of maximal embedding dimension and several families of numerical semigroups generated by arithmetic sequences. Furthermore, we show that which player wins on a given numerical semigroup is a decidable question. Finally, we extend several of our results to the more general setting of subsemigroups of , where is a finite abelian group.
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Accepted:
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DOI: 10.5802/alco.16
Keywords: chomp game, poset game, infinite poset, numerical semigroup, symmetric semigroup, Apéry set
@article{ALCO_2018__1_3_371_0, author = {Garc{\'\i}a-Marco, Ignacio and Knauer, Kolja}, title = {Chomp on numerical semigroups}, journal = {Algebraic Combinatorics}, pages = {371--394}, publisher = {MathOA foundation}, volume = {1}, number = {3}, year = {2018}, doi = {10.5802/alco.16}, zbl = {06897706}, mrnumber = {3856529}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/alco.16/} }
TY - JOUR AU - García-Marco, Ignacio AU - Knauer, Kolja TI - Chomp on numerical semigroups JO - Algebraic Combinatorics PY - 2018 SP - 371 EP - 394 VL - 1 IS - 3 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.16/ DO - 10.5802/alco.16 LA - en ID - ALCO_2018__1_3_371_0 ER -
García-Marco, Ignacio; Knauer, Kolja. Chomp on numerical semigroups. Algebraic Combinatorics, Volume 1 (2018) no. 3, pp. 371-394. doi : 10.5802/alco.16. http://archive.numdam.org/articles/10.5802/alco.16/
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