Neil J. Y. Fan

activity

20102022

most citedBumpless Pipedreams, Reduced Word Tableaux and Stanley Symmetric Functions

4 citations · 7 across the 15 of their papers we have counts for

collaborators

22 papers

math.CO2022★ 2 cited

Pieri and Murnaghan--Nakayama type Rules for Chern classes of Schubert Cells

Neil J. Y. Fan, Peter L. Guo, Rui Xiong

We develop Pieri type as well as Murnaghan--Nakayama type formulas for equivariant Chern--Schwartz--MacPherson classes of Schubert cells in the classical flag variety. These formul…

math.CO2021

Poincaré Polynomials of Odd Diagram Classes

Neil J. Y. Fan, Peter L. Guo

An odd diagram class is a set of permutations with the same odd diagram. Brenti, Carnevale and Tenner showed that each odd diagram class is an interval in the Bruhat order. They co…

math.CO2021

On the Ehrhart Polynomial of Schubert Matroids

Neil J. Y. Fan, Yao Li

In this paper, we give a formula for the number of lattice points in the dilations of Schubert matroid polytopes. As applications, we obtain the Ehrhart polynomials of uniform and…

math.CO2021

Quantized cohomological Hall algebra of the $d$ -loop quiver revisited

Neil J. Y. Fan, Changjian Fu, Liangang Peng

Let $Λ$ be the set of partitions of length $\geq 0$ . We introduce an $N$ -graded algebra $A_{q}^{d} (Λ)$ associated to $Λ$ , which can be viewed as a quantization of the…

math.CO2020

An Involution on Semistandard Skyline Fillings

Neil J. Y. Fan, Peter L. Guo, Nicolas Y. Liu

Non-attacking skyline fillings were used by Haglund, Haiman and Loehr to establish a combinatorial formula for nonsymmetric Macdonald polynomials. Semistandard skyline fillings are…

math.CO2020

Inversion arrangements and the weak Bruhat order

Neil J. Y. Fan

For each permutation $w$ , we can construct a collection of hyperplanes $A_{w}$ according to the inversions of $w$ , which is called the inversion hyperplane arrangement asso…

math.CO2020

Complements of Schubert polynomials

Neil J. Y. Fan, Peter L. Guo, Nicolas Y. Liu

Let $S_{w} (x)$ be the Schubert polynomial for a permutation $w$ of ${1, 2, \dots, n}$ . For any given composition $μ$ , we say that $x^{μ} S_{w} (x^{- 1})$ is the comple…

math.CO2019

Lattice Points in the Newton Polytopes of Key Polynomials

Neil J. Y. Fan, Peter L. Guo, Simon C. Y. Peng +1

We confirm a conjecture of Monical, Tokcan and Yong on a characterization of the lattice points in the Newton polytopes of key polynomials.

math.CO2019

Vertices of Schubitopes

Neil J. Y. Fan, Peter L. Guo

Schubitopes were introduced by Monical, Tokcan and Yong as a specific family of generalized permutohedra. It was proven by Fink, Mészáros and St.Dizier that Schubitopes are the…

math.CO2019

Upper Bounds of Schubert Polynomials

Neil J. Y. Fan, Peter L. Guo

Let $w$ be a permutation of ${1, 2, \dots, n}$ , and let $D (w)$ be the Rothe diagram of $w$ . The Schubert polynomial $S_{w} (x)$ can be realized as the dual character of th…

math.CO2019

Set-valued Rothe Tableaux and Grothendieck Polynomials

Neil J. Y. Fan, Peter L. Guo

The notion of set-valued Young tableaux was introduced by Buch in his study of the Littlewood-Richardson rule for stable Grothendieck polynomials. Knutson, Miller and Yong showed t…

math.CO2018

A Note on Specializations of Grothendieck Polynomials

Neil J. Y. Fan, Peter L. Guo

Buch and Rimányi proved a formula for specializations of double Grothendieck polynomials based on the Yang-Baxter equation related to the degenerate Hecke algebra. A geometric proo…

math.CO2018★ 4 cited

Bumpless Pipedreams, Reduced Word Tableaux and Stanley Symmetric Functions

Neil J. Y. Fan, Peter L. Guo, Sophie C. C. Sun

Lam, Lee and Shimozono introduced the structure of bumpless pipedreams in their study of back stable Schubert calculus. They found that a specific family of bumpless pipedreams, ca…

math.CO2018

Proof of a Conjecture of Reiner-Tenner-Yong on Barely Set-valued Tableaux

Neil J. Y. Fan, Peter L. Guo, Sophie C. C. Sun

The notion of a barely set-valued semistandard Young tableau was introduced by Reiner, Tenner and Yong in their study of the probability distribution of edges in the Young lattice…

math.CO2016

Standard Rothe Tableaux

Neil J. Y. Fan

Edelman and Greene constructed a bijection between the set of standard Young tableaux and the set of balanced Young tableaux of the same shape. Fomin, Greene, Reiner and Shimozono…

math.CO2015

On parabolic Kazhdan-Lusztig R-polynomials for the symmetric group

Neil J. Y. Fan, Peter L. Guo, Grace L. D. Zhang

Parabolic $R$ -polynomials were introduced by Deodhar as parabolic analogues of ordinary $R$ -polynomials defined by Kazhdan and Lusztig. In this paper, we are concerned with the com…

math.CO2013

A Class of Kazhdan-Lusztig R-Polynomials and q-Fibonacci Numbers

William Y. C. Chen, Neil J. Y. Fan, Peter L. Guo +1

Let $S_{n}$ denote the symmetric group on ${1, 2, \dots, n}$ . For two permutations $u, v \in S_{n}$ such that $u \leq v$ in the Bruhat order, let $R_{u, v} (q)$ and $R_{u, v} (q)$ denote th…

math.CO2013

Combinatorial Proof of the Inversion Formula on the Kazhdan-Lusztig R-Polynomials

William Y. C. Chen, Neil J. Y. Fan, Alan J. X. Guo +3

Let $W$ be a Coxeter group, and for $u, v \in W$ , let $R_{u, v} (q)$ be the Kazhdan-Lusztig $R$ -polynomial indexed by $u$ and $v$ . In this paper, we present a combinatorial proof of th…

math.CO2010★ 1 cited

Partitions and Partial Matchings Avoiding Neighbor Patterns

William Y. C. Chen, Neil J. Y. Fan, Alina F. Y. Zhao

We obtain the generating functions for partial matchings avoiding neighbor alignments and for partial matchings avoiding neighbor alignments and left nestings. We show that there i…

math.CO2010

Labeled Ballot Paths and the Springer Numbers

William Y. C. Chen, Neil J. Y. Fan, Jeffrey Y. T. Jia

The Springer numbers are defined in connection with the irreducible root systems of type $B_{n}$ , which also arise as the generalized Euler and class numbers introduced by Shanks. Co…

math.NT2010

The Generating Function for the Dirichlet Series $L_{m} (s)$

William Y. C. Chen, Neil J. Y. Fan, Jeffrey Y. T. Jia

The Dirichlet series $L_{m} (s)$ are of fundamental importance in number theory. Shanks defined the generalized Euler and class numbers in connection with these Dirichlet series, deno…

math.CO2010

Han's Bijection via Permutation Codes

William Y. C. Chen, Neil J. Y. Fan, Teresa X. S. Li

We show that Han's bijection when restricted to permutations can be carried out in terms of the cyclic major code and the cyclic inversion code. In other words, it maps a permutati…

Pieri and Murnaghan--Nakayama type Rules for Chern classes of Schubert Cells

Poincaré Polynomials of Odd Diagram Classes

On the Ehrhart Polynomial of Schubert Matroids

Quantized cohomological Hall algebra of the d-loop quiver revisited

An Involution on Semistandard Skyline Fillings

Inversion arrangements and the weak Bruhat order

Complements of Schubert polynomials

Lattice Points in the Newton Polytopes of Key Polynomials

Vertices of Schubitopes

Upper Bounds of Schubert Polynomials

Set-valued Rothe Tableaux and Grothendieck Polynomials

A Note on Specializations of Grothendieck Polynomials

Bumpless Pipedreams, Reduced Word Tableaux and Stanley Symmetric Functions

Proof of a Conjecture of Reiner-Tenner-Yong on Barely Set-valued Tableaux

Standard Rothe Tableaux

On parabolic Kazhdan-Lusztig R-polynomials for the symmetric group

A Class of Kazhdan-Lusztig R-Polynomials and q-Fibonacci Numbers

Combinatorial Proof of the Inversion Formula on the Kazhdan-Lusztig R-Polynomials

Partitions and Partial Matchings Avoiding Neighbor Patterns

Labeled Ballot Paths and the Springer Numbers

The Generating Function for the Dirichlet Series Lm​(s)

Han's Bijection via Permutation Codes

Quantized cohomological Hall algebra of the $d$ -loop quiver revisited

The Generating Function for the Dirichlet Series $L_{m} (s)$