Paley-type matrices and 1-factorizations of complete graphs

2026/01/18 by Chi Hoi Yip, Semin Yoo · 1 voice
Mathematics · #math.CO #math.NT

paper · pdf

Abstract

Ball, Ortega--Moreno, and Prodromou asked whether, for every odd prime p, one can find a 1-factor of the complete graph K_p+1 with some arithmetic restrictions related to quadratic residues. This problem is motivated by 1-factorizations that are compatible with the sign pattern of certain Paley-type matrices. Recently, Afifurrahman et al. made some partial progress. In this paper, we completely resolve the problem.

Citations

• Approximate formulas for some functions of prime numbers

Discussions

• #New_arXiv_paper Chi Hoi Yip and *Semin Yoo*, Paley-type matrices and 1-factorizations of complete graphs, 2026. arxiv.org/abs/2601.12250 [bsky, 0 points, 0 comments]

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