2025/06/05 by Sarah Miller, Davies, Alfie, Miller, Sarah +2
Computer Science · Mathematics · #20K27 (Secondary) #20M14 #91A46 (Primary) 06F05 #Advanced Topology and Set Theory #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2506.05257
openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Milley and Renault proved an interesting characterisation of invertible elements in the dead-ending universe: they are the games with no subpositions of outcome \mathscrP (the '\mathscrP-free' games). We generalise their approach to obtain a stronger result and show in particular that the set of \mathscrP-free blocking games is closed under addition, which yields that every \mathscrP-free blocking game is invertible modulo the blocking universe. This has consequences for the invertible subgroups of various other misère monoids.