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arXiv · 2503.09325

$λ$-fold near-factorizations of groups

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

We initiate the study of $λ$-fold near-factorizations of groups with $λ> 1$. While $λ$-fold near-factorizations of groups with $λ= 1$ have been studied in numerous papers, this is the first detailed treatment for $λ> 1$. We establish fundamental properties of $λ$-fold near-factorizations and introduce the notion of equivalence. We prove various necessary conditions of $λ$-fold near-factorizations, including upper bounds on $λ$. We present three constructions of infinite families of $λ$-fold near-factorizations, highlighting the characterization of two subfamilies of $λ$-fold near-factorizations. We discuss a computational approach to $λ$-fold near-factorizations and tabulate computational results for abelian groups of small order.

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Donald L. Kreher, Shuxing Li, Douglas R. Stinson. 2025-04-22. $λ$-fold near-factorizations of groups. https://arxiv.org/abs/2503.09325

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