42 citations · 261 across the 125 of their papers we have counts for
141 papers
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…
A Context-free Grammar for the -Positivity of the Trivariate Second-order Eulerian Polynomials
William Y. C. Chen, Amy M. Fu
Ma-Ma-Yeh made a beautiful observation that a transformation of the grammar of Dumont instantly leads to the -positivity of the Eulerian polynomials. We notice that the transfor…
Cubic Equations Through the Looking Glass of Sylvester
William Y. C. Chen
One can hardly believe that there is still something to be said about cubic equations. To dodge this doubt, we will instead try and say something about Sylvester. He doubtless foun…
Semi-invariants of Binary Forms and Sylvester's Theorem
William Y. C. Chen, Ivy D. D. Jia
We obtain a combinatorial formula related to the shear transformation for semi-invariants of binary forms, which implies the classical characterization of semi-invariants in terms…