Exact Covering-Pairing Thresholds for Five-in-a-Row with Two-Parameter Step Sets

A covering pairing for five-in-a-row is a set of disjoint pairs of boardpositions such that every winning line contains one of the pairs; it isa drawing strategy for the second player. For integers \(1\le p 1\) whose prime factors are all \(1\pmod4\) the twometric thresholds eventually coincide.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-01
DOI
https://doi.org/10.5281/zenodo.23089441
Primary Topic
graph theory and CDMA systems
Type
preprint
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preprint

Exact Covering-Pairing Thresholds for Five-in-a-Row with Two-Parameter Step Sets

Hyeon-Seung Cheon
Zenodo (CERN European Organization for Nuclear Research)
graph theory and CDMA systems
preprint

Exact Covering-Pairing Thresholds for Five-in-a-Row with Two-Parameter Step Sets

Hyeon-Seung Cheon
preprint en

Abstract

A covering pairing for five-in-a-row is a set of disjoint pairs of boardpositions such that every winning line contains one of the pairs; it isa drawing strategy for the second player. For integers \(1\le p 1\) whose prime factors are all \(1\pmod4\) the twometric thresholds eventually coincide.

Zenodo (CERN European Organization for Nuclear Research)
graph theory and CDMA systems
DOIOpen Access PDFOpenAlex
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Exact Covering-Pairing Thresholds for Five-in-a-Row with Two-Parameter Step Sets — Hyeon-Seung Cheon · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS