4 papers
Noncrossing Trees and Noncrossing Graphs
William Y. C. Chen, Sherry H. F. Yan
We give a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation of a formula on noncrossing trees and symmetric ternary trees in answer to a…
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…
Matchings Avoiding Partial Patterns
William Y. C. Chen, Toufik Mansour, Sherry H. F. Yan
We show that matchings avoiding certain partial patterns are counted by the 3-Catalan numbers. We give a characterization of 12312-avoiding matchings in terms of restrictions on th…
Weighted 2-Motzkin Paths
William Y. C. Chen, Sherry H. F. Yan, Laura L. M. Yang
This paper is motivated by two problems recently proposed by Coker on combinatorial identities related to the Narayana polynomials and the Catalan numbers. We find that a bijection…