2024/10/09 by Vishal Yadav, Davies, Alfie, Yadav, Vishal · 1 citation
Computer Science · Mathematics · #20M10 (Secondary) #91A46 (Primary) 06F05 #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical and Theoretical Analysis #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2410.06924
openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.