A series of identities for the coefficients of inverse matrices on a Hamming scheme
Let \((U,\{R_0,R_1,\dots,R_n\})\) be an association scheme with \(n\) classes on a finite set \(U=\{u_1,\dots,u_v\}\). Let \(D_i=(d^{(i)}_{kl})\) be a \((v\times v)\)-matrix such that \(d^{(i)}_{kl}=1\), if \((u_k,u_l)\in R_i\), \(0\) otherwise. Let \(F=\{0,1,\dots,q-1\}\), \(U= F^n\), \(x\in U\). This paper establishes the explicit formula of \((\sum^n_{i=0} x^i D_i)^{-1}\) and a series of identities concerned with the coefficients \(b_i\) of the inverse matrix \(\sum^n_{i=0} b_i D_i=(D_0+xD_1)^{-1}\) on a Hamming scheme \(U\).
scientific article; zbMATH DE number 932568