3 citations · 4 across the 10 of their papers we have counts for
9 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…
Stable Equivalences of Giambelli Type Matrices of Schur Functions
William Y. C. Chen, Arthur L. B. Yang
By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli type matrices of a skew Schur function are stably equivalent to…
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
William Y. C. Chen, Louis W. Shapiro, Laura L. M. Yang
The problem of counting plane trees with edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Sta…