The arithmetic-periodicity of CUT for C={1,2c}
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...
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th-mahidol.851082023-06-19T00:27:44Z The arithmetic-periodicity of CUT for C={1,2c} Ellis P. Mahidol University Mathematics 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. (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={1,2c1,2c2,2c3,…}, where c1,c2,…≥2. 2023-06-18T17:27:44Z 2023-06-18T17:27:44Z 2022-12-15 Article Discrete Applied Mathematics Vol.322 (2022) , 391-403 10.1016/j.dam.2022.08.027 0166218X 2-s2.0-85144086362 https://repository.li.mahidol.ac.th/handle/123456789/85108 SCOPUS |
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Mathematics Ellis P. The arithmetic-periodicity of CUT for C={1,2c} |
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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. (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={1,2c1,2c2,2c3,…}, where c1,c2,…≥2. |
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Mahidol University |
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Mahidol University Ellis P. |
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Article |
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Ellis P. |
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Ellis P. |
| title |
The arithmetic-periodicity of CUT for C={1,2c} |
| title_short |
The arithmetic-periodicity of CUT for C={1,2c} |
| title_full |
The arithmetic-periodicity of CUT for C={1,2c} |
| title_fullStr |
The arithmetic-periodicity of CUT for C={1,2c} |
| title_full_unstemmed |
The arithmetic-periodicity of CUT for C={1,2c} |
| title_sort |
arithmetic-periodicity of cut for c={1,2c} |
| publishDate |
2023 |
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https://repository.li.mahidol.ac.th/handle/123456789/85108 |
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1781415286347399168 |