WEIGHTED INCREASING TREES, EXPONENTIAL RIORDAN MATRICES, AND MOMENTS

摘要

Using weighted increasing trees, we give combinatorial representations of exponential generating functions that are used in Riordan Matrices. The Stieltjes matrix of a Riordan matrix contains important information concerning the weights for the increasing trees. We give an explicit formula for the Stieltjes matrix of a Riordan matrix. Several examples are given that illustrate the relationship between weighted increasing trees and some permutations. We also interpret the entries and moments of some Riordan matrices in terms of increasing trees and permutations.