ALGEBRAIC COMBINATORICS

no. 3
Chomp on numerical semigroups
García-Marco, Ignacio1; Knauer, Kolja2
1 Facultad de Ciencias, Universidad de La Laguna. 38200 La Laguna, Spain
2 Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France
Algebraic Combinatorics, Volume 1 (2018) no. 3, pp. 371-394.

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 ℕ×T, where T is a finite abelian group.

Received:
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Accepted:
Published online:
DOI: 10.5802/alco.16
Classification: 05E40, 91A46, 06A07
Keywords: chomp game, poset game, infinite poset, numerical semigroup, symmetric semigroup, Apéry set
García-Marco, Ignacio 1; Knauer, Kolja 2

1 Facultad de Ciencias, Universidad de La Laguna. 38200 La Laguna, Spain
2 Aix Marseille Univ, Université de Toulon, CNRS, LIS, Marseille, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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García-Marco, Ignacio; Knauer, Kolja. Chomp on numerical semigroups. Algebraic Combinatorics, Volume 1 (2018) no. 3, pp. 371-394. doi : 10.5802/alco.16. https://alco.centre-mersenne.org/articles/10.5802/alco.16/

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