12 citations · 20 across the 17 of their papers we have counts for
17 papers · 1 filter
Weighted Forms of Euler's Theorem
William Y. C. Chen, Kathy Q. Ji
In answer to a question of Andrews about finding combinatorial proofs of two identities in Ramanujan's "Lost" Notebook, we obtain weighted forms of Euler's theorem on partitions wi…
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…
Nonterminating Basic Hypergeometric Series and the -Zeilberger Algorithm
William Y. C. Chen, Qing-Hu Hou, Yan-Ping Mu
We present a systematic method for proving nonterminating basic hypergeometric identities. Assume that is the summation index. By setting a parameter to , we may find…
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…
Stanley's Zrank Problem on Skew Partitions
William Y. C. Chen, Arthur L. B. Yang
We present an affirmative answer to Stanley's zrank problem, namely, the zrank and rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices…
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…