2000 character limit reached
Isomorphism Theorems for Impartial Combinatorial Games (2505.04919v1)
Published 8 May 2025 in math.CO
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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.