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$\lambda$-fold near-factorizations of groups
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abstract
We initiate the study of $\lambda$-fold near-factorizations of groups with $\lambda > 1$. While $\lambda$-fold near-factorizations of groups with $\lambda = 1$ have been studied in numerous papers, this is the first detailed treatment for $\lambda > 1$. We establish fundamental properties of $\lambda$-fold near-factorizations and introduce the notion of equivalence. We prove various necessary conditions of $\lambda$-fold near-factorizations, including upper bounds on $\lambda$. We present three constructions of infinite families of $\lambda$-fold near-factorizations, highlighting the characterization of two subfamilies of $\lambda$-fold near-factorizations. We discuss a computational approach to $\lambda$-fold near-factorizations and tabulate computational results for abelian groups of small order.
Forward citations
Cited by 2 Pith papers
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On Matrix Product Factorization in Association Schemes
In symmetric association schemes, matrix-product factorizations A_S A_T = A_U are characterized by spectral subset-sum conditions; rigidity forces the universal pentagon case to be the 5-cycle, and Hamming schemes adm...
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Cyclotomic construction of $\lambda$-fold near-factorizations of cyclic groups
For primes p = 4n^4 + 12n^2 + 1, four explicit pairs of unions of order-8 cyclotomic cosets in F_p are shown to be (p-1)/16-fold near-factorizations.
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