19 citations · 92 across the 66 of their papers we have counts for
7 papers · 2 filters
Decomposition of Triply Rooted Trees
William Y. C. Chen, Janet F. F. Peng, Harold R. L. Yang
In this paper, we give a decomposition of triply rooted trees into three doubly rooted trees. This leads to a combinatorial interpretation of an identity conjectured by Lacasse in…
On Pattern Avoiding Alternating Permutations
Joanna N. Chen, William Y. C. Chen, Robin D. P. Zhou
An alternating permutation of length is a permutation such that . Let denote set of alternating permutations of ${1,2,...…
Proof of Lassalle's Positivity Conjecture on Schur Functions
William Y. C. Chen, Anne X. Y. Ren, Arthur L. B. Yang
In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let denote the rising factorial,…
On the Number of Partitions with Designated Summands
William Y. C. Chen, Kathy Q. Ji, Hai-Tao Jin +1
Andrews, Lewis and Lovejoy introduced the partition function PD(n) as the number of partitions of with designated summands, where we assume that among parts with equal size, ex…
Disposition Polynomials and Plane Trees
William Y. C. Chen, Janet F. F. Peng
We define the disposition polynomial as . When , this polynomial becomes the generating function of plane t…
Context-free Grammars and Multivariate Stable Polynomials over Stirling Permutations
William Y. C. Chen, Robert X. J. Hao, Harold R. L. Yang
Recently, Haglund and Visontai established the stability of the multivariate Eulerian polynomials as the generating polynomials of the Stirling permutations, which serves as a unif…