Abstract
Using the algebraic techniques of formal series, we obtain a combinatorial decomposition of some matrices generated by the generalized rencontres polynomials. Specifically, for the complete matrix and the Hankel matrix we obtain an LDU-decomposition RDST, where D is a diagonal matrix and R and S are two Sheffer matrices. Then, for the shifted matrices we obtain an LTU-decomposition RTST, where T is a tridiagonal matrix and R and S are two Sheffer matrices. Furthermore, we give an algebraic characterization of the generalized rencontres numbers and polynomials in terms of Hankel determinants. Finally, we determine a relation between the complete matrices and the Hankel matrices.
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