The spectrum of nim-values for achievement games for generating finite groups
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| Format: | Preprint |
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2020
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| _version_ | 1866917585194319872 |
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| author | Benesh, Bret J. Ernst, Dana C. Sieben, Nandor |
| author_facet | Benesh, Bret J. Ernst, Dana C. Sieben, Nandor |
| contents | We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The game ends when the jointly selected elements generate the group. The last player able to make a move is the winner of the game. We prove that the spectrum of nim-values of these games is $\{0,1,2,3,4\}$. This positively answers two conjectures from a previous paper by the last two authors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_08980 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The spectrum of nim-values for achievement games for generating finite groups Benesh, Bret J. Ernst, Dana C. Sieben, Nandor Group Theory Combinatorics 91A46, 20D30 We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The game ends when the jointly selected elements generate the group. The last player able to make a move is the winner of the game. We prove that the spectrum of nim-values of these games is $\{0,1,2,3,4\}$. This positively answers two conjectures from a previous paper by the last two authors. |
| title | The spectrum of nim-values for achievement games for generating finite groups |
| topic | Group Theory Combinatorics 91A46, 20D30 |
| url | https://arxiv.org/abs/2004.08980 |