139 citations
- Lyon 1 UniversitéFR4 papers
- Massachusetts Institute of TechnologyUS4 papers
- Institut Camille JordanFR3 papers
- East China Normal UniversityCN2 papers
- Howard UniversityUS2 papers
- University of California, IrvineUS2 papers
- China Center of Advanced Science and TechnologyCN1 paper
- Chinese Academy of SciencesCN1 paper
- Dalian University of TechnologyCN1 paper
- École PolytechniqueFR1 paper
- Institute of High Energy PhysicsCN1 paper
- Institute of Theoretical PhysicsCN1 paper
22 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…
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…
The Zrank Conjecture and Restricted Cauchy Matrices
Guo-Guang Yan, Arthur L. B. Yang, Joan J. Zhou
The rank of a skew partition , denoted , is the smallest number such that is a disjoint union of border strips. Let denote the skew Sch…
Division and the Giambelli Identity
Susan Y. J. Wu, Arthur L. B. Yang
Given two polynomials f(x) and g(x), we extend the formula expressing the remainder in terms of the roots of these two polynomials to the case where f(x) is a Laurent polynomial. T…