2 citations · 3 across the 5 of their papers we have counts for
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Labeled Plane Trees and Increasing Plane Trees
Lora R. Du, Kathy Q. Ji, Dax T. X. Zhang
The main aim of this paper is to establish a polynomial analogue of (with as the -th Catalan number) in the setting of labeled plane trees and incr…
Involutions on Tip-Augmented Plane Trees for Leaf Interchanging
Laura L. M. Yang, Dax T. X. Zhang
This paper constructs two involutions on tip-augmented plane trees, as defined by Donaghey, that interchange two distinct types of leaves while preserving all other leaves. These t…
New refinements of Narayana polynomials and Motzkin polynomials
Janet J. W. Dong, Lora R. Du, Kathy Q. Ji +1
Chen, Deutsch and Elizalde introduced a refinement of the Narayana polynomials by distinguishing between old (leftmost child) and young leaves of plane trees. They also provided a…
Signed Mahonian Polynomials on Derangements in Classical Weyl Groups
Kathy Q. Ji, Dax T. X. Zhang
The polynomial of the major index over the subset of the Coxeter group is called the Mahonian polynomial over , where is a Mahonian s…
A Cyclic Analogue of Stanley's Shuffle Theorem
Kathy Q. Ji, Dax T. X. Zhang
We introduce the cyclic major index of a cycle permutation and give a bivariate analogue of enumerative formula for the cyclic shuffles with a given cyclic descent numbers due to A…
Some Refinements of Stanley's Shuffle Theorem
Kathy Q. Ji, Dax T. X. Zhang
We first give a combinatorial proof of Stanley's shuffle theorem by using the insertion lemma of Haglund, Loehr and Remmel. Based on this combinatorial construction, we establish s…