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.
@article{10_37236_13504,
author = {Alfie Davies and Vishal Yadav},
title = {Invertibility in the mis\`ere multiverse},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {4},
doi = {10.37236/13504},
zbl = {8120096},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13504/}
}
TY - JOUR
AU - Alfie Davies
AU - Vishal Yadav
TI - Invertibility in the misère multiverse
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/13504/
DO - 10.37236/13504
ID - 10_37236_13504
ER -
%0 Journal Article
%A Alfie Davies
%A Vishal Yadav
%T Invertibility in the misère multiverse
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/13504/
%R 10.37236/13504
%F 10_37236_13504
Alfie Davies; Vishal Yadav. Invertibility in the misère multiverse. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13504
