2025/03/12 by Kreher, Donald L., Li, Shuxing, Stinson, Douglas R.
#05B10 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2503.09325
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.