Invertibility in the mis\`ere multiverse
Combinatorics
2024-10-10 v1
Abstract
Understanding invertibility in restricted mis\`ere 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.
Cite
@article{arxiv.2410.06924,
title = {Invertibility in the mis\`ere multiverse},
author = {Alfie Davies and Vishal Yadav},
journal= {arXiv preprint arXiv:2410.06924},
year = {2024}
}
Comments
31 pages