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.
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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.