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arXiv · 2610.15826

The theory of $(λ,μ)$-fold factorizations of groups

Donald L. Kreher·Shuxing Li·Douglas R. Stinson
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Abstract

Motivated by the recent study of $λ$-fold near-factorizations of finite groups by Kreher, Li, and Stinson (Designs, Codes and Cryptography, 2026), we introduce and systematically investigate $(λ,μ)$-fold factorizations of finite groups, with particular emphasis on the abelian case. These structures form a natural relaxation of $λ$-fold near-factorizations and encompass several related families that have previously been studied in different contexts. We establish the foundational theory of $(λ,μ)$-fold factorizations, provide two general constructions, and prove several nonexistence results for finite abelian groups.

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Donald L. Kreher, Shuxing Li, Douglas R. Stinson. 2026-10-11. The theory of $(λ,μ)$-fold factorizations of groups. https://arxiv.org/abs/2610.15826

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