74 citations · 186 across the 16 of their papers we have counts for
17 papers
Continuous Narayana Interpolations: Hankel Total Positivity and Log-Convexity Preservation
Jiang Zeng
We study a continuous interpolation between the type and shifted type Narayana triangles. Using a direct Gegenbauer-moment proof and a continuant comparison criterion, we s…
Enumeration of permutations by the parity of descent positions
Qiongqiong Pan, Jiang Zeng
Noticing that some recent variations of descent polynomials are special cases of Carlitz and Scoville's four-variable polynomials, which enumerate permutations by the parity of des…
Counting derangements with signed right-to-left minima and excedances
Yanni Pei, Jiang Zeng
Recently Alexandersson and Getachew proved some multivariate generalizations of a formula for enumerating signed excedances in derangements. In this paper we first relate their wor…
Cycles of even-odd drop permutations and continued fractions of Genocchi numbers
Qiongqiong Pan, Jiang Zeng
Recently, Lazar and Wachs (arXiv:1910.07651) showed that the (median) Genocchi numbers play a fundamental role in the study of the homogenized Linial arrangement and obtained two n…
Equidistributions around special kinds of descents and excedances
Bin Han, Jianxi Mao, Jiang Zeng
We consider a sequence of four variable polynomials by refining Stieltjes' continued fraction for Eulerian polynomials. Using combinatorial theory of Jacobi-type continued fraction…
Moments of q-Jacobi Polynomials and q-Zeta Values
Frédéric Chapoton, Christian Krattenthaler, Jiang Zeng
We explore some connections between moments of rescaled little q-Jacobi polynomials, q-analogues of values at negative integers for some Dirichlet series, and the q-Eulerian polyno…
Minor summation formula of hyperpfaffians and Selberg integrals
Masao Ishikawa, Jiang Zeng
In the previous paper (J. Combin. Theory Ser. A, 120, 2013, 1263--1284) H. Tagawa and the two authors proposed an algebraic method to compute certain Pfaffians whose form resemble…
Equidistributions of mesh patterns of length two and Kitaev and Zhang's conjectures
Bin Han, Jiang Zeng
A systematic study of avoidance of mesh patterns of length 2 was conducted by Hilmarsson et al. in 2015. In a recent paper Kitaev and Zhang examined the distribution of the aforeme…
More bijections for Entringer and Arnold families
Heesung Shin, Jiang Zeng
The Euler number (resp. Entringer number ) enumerates the alternating (down-up) permutations of (resp. starting with ). The Springer number …
Gap between the largest and smallest parts of partitions and Berkovich and Uncu's conjectures
Wenston J. T. Zang, Jiang Zeng
We prove three main conjectures of Berkovich and Uncu (Ann. Comb. 23 (2019) 263--284) on the inequalities between the numbers of partitions of with bounded gap between largest…
Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions
Alan D. Sokal, Jiang Zeng
We find Stieltjes-type and Jacobi-type continued fractions for some "master polynomials" that enumerate permutations, set partitions or perfect matchings with a large (sometimes in…
Further equidistribution of set-valued statistics on permutations
Jianxi Mao, Jiang Zeng
We construct bijections to show that two pairs of sextuple set-valued statistics of permutations are equidistributed on symmetric groups. This extends a recent result of Sokal and…
Brändén's -Eulerian polynomials, André permutations and continued fractions
Qiong Qiong Pan, Jiang Zeng
In 2008 Brändén proved a -analogue of the -expansion formula for Eulerian polynomials and conjectured the divisibility of the -coefficient by .…
Eulerian polynomials and excedance statistics
Bin Han, Jianxi Mao, Jiang Zeng
A formula of Stembridge states that the permutation peak polynomials and descent polynomials are connected via a quadratique transformation. The aim of this paper is to establish t…
Combinatorics of -Laguerre polynomials and their moments
Qiongqiong Pan, Jiang Zeng
We consider a -analogue of Laguerre polynomials for integral , which turns out to be a rescaled version of Al-Salam--Chihara polynomials. A comb…
The symmetric and unimodal expansion of Eulerian polynomials via continued fractions
Heesung Shin, Jiang Zeng
This paper was motivated by a conjecture of Brändén (European J. Combin. \textbf{29} (2008), no.~2, 514--531) about the divisibility of the coefficients in an expansion of generali…
The -tangent and -secant numbers via continued fractions
Heesung Shin, Jiang Zeng
It is well known that the -evaluation of the enumerator polynomials of permutations (resp. derangements) by the number of excedances gives rise to tangent numbers (resp. seca…