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 admit no nontrivial factorization of the studied form.
Cyclotomic construction of $\lambda$-fold near-factorizations of cyclic groups
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abstract
The study of near-factorizations of finite groups dates back to the 1950s. Recently, this topic has attracted renewed attention, and the concept has been extended to $\lambda$-fold near-factorizations, in which each non-identity group element appears exactly $\lambda \ge 1$ times. This paper presents a cyclotomic construction of $\lambda$-fold near-factorizations in the cyclic group $\mathbb{F}_p$, where $p = 4n^4 + 12n^2 + 1$ is prime for $n \ge 1$.
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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 admit no nontrivial factorization of the studied form.