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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Vydáno v:Communications in algebra Ročník 53; číslo 10; s. 4053 - 4062
Hlavní autoři: Bras-Amorós, Maria, Moskowitz, Gilad, Ponomarenko, Vadim
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 03.10.2025
Taylor & Francis Ltd
Témata:
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
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Abstract 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.
AbstractList 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.
Author Ponomarenko, Vadim
Bras-Amorós, Maria
Moskowitz, Gilad
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Cites_doi 10.1016/j.jalgebra.2024.10.028
10.1016/j.jpaa.2003.10.024
10.1080/00029890.2020.1785254
10.1007/s00233-002-0007-3
10.1090/mcom/3075
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References e_1_3_2_8_1
e_1_3_2_7_1
Berlekamp E. R. (e_1_3_2_2_1) 1982
Moskowitz G. (e_1_3_2_9_1) 2021
Rosales J. C. (e_1_3_2_10_1) 2008; 34
Rosales J. C. (e_1_3_2_11_1) 2009
Eaton R. (e_1_3_2_6_1) 2023; 23
e_1_3_2_12_1
e_1_3_2_5_1
e_1_3_2_13_1
e_1_3_2_4_1
e_1_3_2_3_1
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  volume-title: Advances In Computer Games: 17th International Conference, ACG 2021, Virtual Event
  year: 2021
  ident: e_1_3_2_9_1
– ident: e_1_3_2_5_1
  doi: 10.1016/j.jalgebra.2024.10.028
– volume-title: Developments in Mathematics
  year: 2009
  ident: e_1_3_2_11_1
– volume-title: Winning Ways, For Your Mathematical Plays
  year: 1982
  ident: e_1_3_2_2_1
– ident: e_1_3_2_3_1
– ident: e_1_3_2_4_1
– volume: 23
  start-page: 1553
  year: 2023
  ident: e_1_3_2_6_1
  article-title: A further investigation of positions in Sylver Coinage for which four has been chosen
  publication-title: Integers
– ident: e_1_3_2_13_1
  doi: 10.1016/j.jpaa.2003.10.024
– volume: 34
  start-page: 339
  issue: 2
  year: 2008
  ident: e_1_3_2_10_1
  article-title: Families of numerical semigroups closed under finite intersections and for the frobenius number
  publication-title: Houston J. Math.
– ident: e_1_3_2_7_1
  doi: 10.1080/00029890.2020.1785254
– ident: e_1_3_2_12_1
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SubjectTerms 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
Title Construction of an endgame rulebook for Sylver Coinage using trees of numerical semigroups
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