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Triple factorization of some Riordan matrices. (English) Zbl 0778.05005

The paper studies the Riordan group, i.e. infinite lower triangular matrices associated with certain generating functions. For such a matrix \(L\), \(\bar L\) denotes \(L\) with the first line deleted. The Stieltjes matrix of \(L\), \(S_ L\), is the (unique) solution of \(LS_ L=\bar L\). The paper shows that if \(S_ L\) is tridiagonal, then \(L\) admits a factorization \(L=PCF\) into special types of matrices. Applications are given to big Schröder numbers and Legendre polynomials.

MSC:

05A15 Exact enumeration problems, generating functions
11C20 Matrices, determinants in number theory
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