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Mind the gap: A real-valued distance on combinatorial games

Year: 2026

Type: preprint

Abstract: We define a real-valued distance metric $wd$ on the space $\mathcal{C}$ of short combinatorial games in canonical form. We demonstrate the existence of Cauchy sequences informed by sidling sequences, find limit points, and investigate the closure $\overline{\mathcal{C}}$, which is shown to partition the set of loopy games in a non-trivial way. Stoppers, enders, and non-stopper-sided loopy games are explored, as well as the topological properties of $(\mathcal{C},wd)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.10574

Authors: Burke, Kyle, Fisher, Michael, Tennenhouse, Craig

Institutions: Florida Southern College, West Chester University, University of New England

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7124456993

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