Construction of an endgame rulebook for Sylver Coinage using trees of numerical semigroups

In this paper we show how the algorithms to explore the tree of numerical semigroups can be used to calculate the winningness of positions in the game of Sylver Coinage. We introduce a new invariant for numerical semigroups, the minimal distance, and show how it can be used to prune the tree of nume...

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Bibliographic Details
Published in:	Communications in algebra Vol. 53; no. 10; pp. 4053 - 4062
Main Authors:	Bras-Amorós, Maria, Moskowitz, Gilad, Ponomarenko, Vadim
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis 03.10.2025 Taylor & Francis Ltd
Subjects:	05A99 None of the above, but in this section (section 05Axx is Enumerative combinatorics) 06F05 Ordered semigroups and monoids 20M14 Commutative semigroups 68W30 Symbolic computation and algebraic computation numerical semigroup Semigroups Sylver coinage game
ISSN:	0092-7872, 1532-4125
Online Access:	Get full text
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Summary:	In this paper we show how the algorithms to explore the tree of numerical semigroups can be used to calculate the winningness of positions in the game of Sylver Coinage. We introduce a new invariant for numerical semigroups, the minimal distance, and show how it can be used to prune the tree of numerical semigroups for an efficient way of calculating the winningness of positions in the game of Sylver Coinage. We end with a few open questions that were spawned as a result of this research.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0092-7872 1532-4125
DOI:	10.1080/00927872.2025.2456089