2 citations · 5 across the 18 of their papers we have counts for
21 papers
A Grammatical Calculus for the Ramanujan Polynomials
William Y. C. Chen, Amy M. Fu, Elena L. Wang
The Ramanujan polynomials arise in three intertwined contexts. As remarked by BerndtEvans-Wilson, no combinatorial perspective seems to be alluded to in the original definition of…
Increasing Binary Trees and the -Eulerian Polynomials
William Y. C. Chen, Amy M. Fu
In light of the grammar given by Ji for the -Eulerian polynomials introduced by Carlitz and Scoville, we provide a labeling scheme for increasing binary trees. In this setti…
A Grammar of Dumont and a Theorem of Diaconis-Evans-Graham
William Y. C. Chen, Amy M. Fu
We came across an unexpected connection between a remarkable grammar of Dumont for the joint distribution of $(\exc, \fix)$ over and a beautiful theorem of Diaconis-Evans-Gra…
A Grammatical Calculus for Peaks and Runs of Permutations
William Y. C. Chen, Amy M. Fu
We develop a nonstandard approach to exploring polynomials associated with peaks and runs of permutations. With the aid of a context-free grammar, or a set of substitution rules, o…
The Dumont Ansatz for the Eulerian Polynomials, Peak Polynomials and Derivative Polynomials
William Y. C. Chen, Amy M. Fu
We observe that three context-free grammars of Dumont can be brought to a common ground, via the idea of transformations of grammars, proposed by Ma-Ma-Yeh. Then we develop a unifi…
The Gessel Correspondence and the Partial -Positivity of the Eulerian Polynomials on Multiset Stirling Permutations
William Y. C. Chen, Amy M. Fu, Sherry H. F. Yan
Pondering upon the grammatical labeling of 0-1-2 increasing plane trees, we come to the realization that the grammatical labels play a role as records of chopped off leaves of the…