Some combinatorial applications of the q-Riordan matrix

-Riordan array for q -Pascal matrix and its inverse matrix

In this paper, we prove the q -analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations ∗q and ∗1/q , we obtain a q -analogue of the Riordan representation of the q -Pascal matrix. In addition, by aid of the q -Lagrange expansion formula we get q -Riordan representation for its inverse matrix.

Matrix Characterizations of Riordan Arrays

Here we discuss two matrix characterizations of Riordan arrays, P -matrix characterization and A-matrix characterization. P -matrix is an extension of the Stieltjes matrix defined in [25] and the production matrix defined in [7]. By modifying the marked succession rule introduced in [18], a combinatorial interpretation of the P -matrix is given. The P -matrix characterizations of some subgroups...

Riordan group approaches in matrix factorizations

In this paper, we consider an arbitrary binary polynomial sequence {A_n} and then give a lower triangular matrix representation of this sequence. As main result, we obtain a factorization of the innite generalized Pascal matrix in terms of this new matrix, using a Riordan group approach. Further some interesting results and applications are derived.

Combinatorial sums and implicit Riordan arrays

In this paper we present the theory of implicit Riordan arrays, that is, Riordan arrays which require the application of the Lagrange Inversion Formula to be dealt with. We show several examples in which our approach gives explicit results, both in finding closed expressions for sums and, especially, in solving classes of combinatorial sum inversions.

Some Applications of Combinatorial Differential Topology