Isomorphism Theorems for Impartial Combinatorial Games
Combinatorics
2025-10-23 v2
Abstract
We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four isomorphism theorems from universal algebra are valid in this category. Quotient optiongraphs, including the minimum quotient, provide simplifications that can help in the analysis of games.
Cite
@article{arxiv.2505.04919,
title = {Isomorphism Theorems for Impartial Combinatorial Games},
author = {Mikhail Baltushkin and Dana C. Ernst and Nándor Sieben},
journal= {arXiv preprint arXiv:2505.04919},
year = {2025}
}
Comments
11 pages, 10 figures