Bin Han

Bin Han
Bar Ilan University | BIU · Department of Mathematics

PhD

About

14
Publications
355
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25
Citations
Introduction
Skills and Expertise
Additional affiliations
December 2019 - present
Bar Ilan University
Position
  • PostDoc Position
Education
October 2015 - November 2019
Claude Bernard University Lyon 1
Field of study
  • Mathematics

Publications

Publications (14)
Article
The binomial Eulerian polynomials, first introduced in work of Postnikov, Reiner and Williams, are γ-positive polynomials and can be interpreted as h-polynomials of certain flag simplicial polytopes. Recently, Athanasiadis studied analogs of these polynomials for colored permutations and proved that they can be written as the sums of two γ-positive...
Article
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 aforementioned patterns. The aim of this paper is to prove more equidistributions of mesh pattern and confirm Kitaev and Zhang's four conjectures by constructing two involutions...
Article
The γ-coefficients of Eulerian polynomials were first considered by Foata and Schützenberger. In this paper, we provide combinatorial interpretations for the γ-coefficients arising from the segmented permutations and segmented derangements via Brändén’s modified Foata–Strehl action. We also give the combinatorial interpretations of γ-coefficients f...
Preprint
In a recent paper ({arXiv:2101.01928v1}) Baril and Kirgizov posed two conjectures on the equidistibution of $(cyc, des_2)\sim (cyc, pex)$ and $(des, des_2)\sim (exc, pex)$, where cyc, des and exc are classical statistics counting the numbers of cycles, descents and excedances of permutation, while $des_2$ and $pex$ are numbers of special descents a...
Article
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 the cycle analogue of Stembridge's formula by using cycle peaks and excedances of permutations. We prove a series of new general formulae expressing polynomials counting p...
Preprint
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 aforementioned patterns. The aim of this paper is to prove more equidistributions of mesh pattern and confirm Kitaev and Zhang's four conjectures by constructing two involutions...
Article
It is well known that the permutation peak polynomials and descent polynomials are connected via a quadratic transformation. By rephrasing the latter formula with permutation cycle peaks and excedances we are able to prove a series of general formulas expressing polynomials counting permutations by various excedance statistics in terms of refined E...
Thesis
The gamma positivity of a combinatorial sequence unifies both unimodality and symmetry. Finding new family of objets whose enumerative sequences have gamma positivity is a challenge and important topic in recent years. it has received considerable attention in recent times because of Gal’s conjecture, which asserts that the gamma-vector has nonnega...
Preprint
A formula of Stembridge states that the permutation peak polynomials and descent polynomials are connected via a quadratique transformation. Rephrasing the latter formula with permutation cycle peaks and excedances we are able to prove a series of general formulas expressing polynomials counting permutations by various excedance statistics in terms...
Article
The aim of this paper is two-fold. We first prove several new interpretations of a kind of (q,t)-Catalan numbers along with their corresponding γ-expansions using pattern avoiding permutations. Secondly, we give a complete characterization of certain (−1)-phenomenon for each subset of permutations avoiding a single pattern of length three, and disc...
Article
Motivated by the λ-Euler’s difference table of Eriksen et al. and colored Euler’s difference table of Faliharimalala and Zeng, we study the λ-analogue of colored Euler’s difference table and generalize their results. We generalize the number of permutations with k-excedances studied by Liese and Remmel in colored permutations. We also extend Wang e...
Preprint
Full-text available
The aim of this paper is two-folded. We first prove several new interpretations of a kind of $q$-Narayana polynomials along with their corresponding $\gamma$-expansions using pattern avoiding permutations. Secondly, we give a complete characterization of certain $(-1)$-phenomenon for all Catalan subsets avoiding a single pattern of length three, an...

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