Invertibility in the misère multiverse
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916429357383680 |
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| author | Davies, Alfie Yadav, Vishal |
| author_facet | Davies, Alfie Yadav, Vishal |
| contents | Understanding invertibility in restricted misère play has been challenging; in particular, the possibility of non-conjugate inverses posed difficulties. Advances have been made in a few specific universes, but a general theorem was elusive. We prove that every universe has the conjugate property, and also give a characterisation of the invertible elements of each universe. We then explore when a universe can have non-trivial invertible elements, leaving a slew of open problems to be further investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invertibility in the misère multiverse Davies, Alfie Yadav, Vishal Combinatorics 91A46 (Primary) 06F05, 20M10 (Secondary) Understanding invertibility in restricted misère play has been challenging; in particular, the possibility of non-conjugate inverses posed difficulties. Advances have been made in a few specific universes, but a general theorem was elusive. We prove that every universe has the conjugate property, and also give a characterisation of the invertible elements of each universe. We then explore when a universe can have non-trivial invertible elements, leaving a slew of open problems to be further investigated. |
| title | Invertibility in the misère multiverse |
| topic | Combinatorics 91A46 (Primary) 06F05, 20M10 (Secondary) |
| url | https://arxiv.org/abs/2410.06924 |