6 papers
On the limiting distribution of the number of improper edges for random trees
Wennie W. J. Ma, Kathy Q. Ji
Improper edges were introduced by Shor to refine Cayley's formula for rooted labeled trees. Zeng established a connection between Shor's refinement and the Ramanujan polynomials. L…
Revisiting -Derangement Numbers via Decorated Permutations
Kathy Q. Ji
This paper aims to provide a direct combinatorial proof of the Gessel-Wachs formula for -derangement numbers in the setting of decorated permutations, without using the -bino…
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…
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…
A Refinement of a Theorem of Diaconis-Evans-Graham
Lora R. Du, Kathy Q. Ji
The note is dedicated to refining a theorem by Diaconis, Evans, and Graham concerning successions and fixed points of permutations. This refinement specifically addresses non-adjac…
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…