18 citations · 67 across the 51 of their papers we have counts for
7 papers · 2 filters
Linked Partitions and Linked Cycles
William Y. C. Chen, Susan Y. J. Wu, Catherine Yan
The notion of noncrossing linked partition arose from the study of certain transforms in free probability theory. It is known that the number of noncrossing linked partitions of [n…
The Abel Lemma and the q-Gosper Algorithm
Vincent Y. B. Chen, William Y. C. Chen, Nancy S. S. Gu
Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey's bilateral summation formula. In other words, the Abel…
Labeled Partitions and the q-Derangement Numbers
William Y. C. Chen, Deheng Xu
By a re-examination of MacMahon's original proof of his celebrated theorem on the distribution of the major indices over permutations, we give a reformulation of his argument in te…
Faulhaber's Theorem on Power Sums
William Y. C. Chen, Amy M. Fu, Iris F. Zhang
We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression…
BG-ranks and 2-cores
William Y. C. Chen, Kathy Q. Ji, Herbert S. Wilf
We find the number of partitions of whose BG-rank is , in terms of , the number of pairs of partitions whose total number of cells is , giving both bijective and g…
Riordan Paths and Derangements
William Y. C. Chen, Eva Y. P. Deng, Laura L. M. Yang
Riordan paths are Motzkin paths without horizontal steps on the x-axis. We establish a correspondence between Riordan paths and -avoiding derangements. We also pr…