4 citations · 9 across the 7 of their papers we have counts for
7 papers
Pseudo-involutions in the Riordan group
Alexander Burstein, Louis W. Shapiro
We consider pseudo-involutions in the Riordan group where the generating function for the first column of a Riordan array satisfies a palindromic or near-palindromic functional…
Mutation effects in ordered trees
Gi-Sang Cheon, Hana Kim, Louis W. Shapiro
A mutation will affect an individual and some or all of its descendants. In this paper, we investigate ordered trees with a distinguished vertex called the mutator. We describe var…
Lattice Polynomials, 12312-Avoiding Partial Matchings and Even Trees
William Y. C. Chen, Louis W. Shapiro, Susan Y. J. Wu
The lattice polynomials are introduced by Hough and Shapiro as a weighted count of certain lattice paths from the origin to the point . In particular, $L_{2n, n…
The Riordan Group and Symmetric Lattice Paths
Li-Hua Deng, Eva Y. P. Deng, Louis W. Shapiro
In this paper, we study symmetric lattice paths. Let , , and denote the number of symmetric Dyck paths, symmetric Motzkin paths, and symmetric Schröder paths…
The Butterfly Decomposition of Plane Trees
William Y. C. Chen, Nelson Y. Li, Louis W. Shapiro
We introduce the notion of doubly rooted plane trees and give a decomposition of these trees, called the butterfly decomposition which turns out to have many applications. From the…
Matrix Identities on Weighted Partial Motzkin Paths
William Y. C. Chen, Nelson Y. Li, Louis W. Shapiro +1
We give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence which has been derived by Shapiro, Woan and Getu by using Ri…