Michael X. X. Zhong

activity

20132026

(s, s + 1, s + 2)

-Core Partitions

2 citations · 2 across the 10 of their papers we have counts for

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11 papers · 1 filter

math.CO2026

Polynomial reduction for $q$ -holonomic sequences

Rong-Hua Wang, Xiao-Ran Yang, Michael X. X. Zhong

This paper provides a (Laurent) polynomial reduction to $q$ -holonomic sequences $F_{k} (q)$ . We first characterize Laurent polynomials $p ~ (x)$ such that the product $\tilde{p}(…

math.CO2025

Congruences for sums of Delannoy numbers and polynomials

Rong-Hua Wang, Michael X. X. Zhong

In this paper, we apply the power-partible reduction to study arithmetic properties of sums involving Delannoy numbers $D_{k}$ and polynomials $D_{k} (z)$ . Let $v\in\bN$ and $p$ be an o…

math.CO2023

Power-partible Reduction and Congruences for Schröder Polynomials

Chen-Bo Jia, Rong-Hua Wang, Michael X. X. Zhong

In this note, we apply the power-partible reduction to show the following arithmetic properties of large Schröder polynomials $S_{n} (z)$ and little Schröder polynomials $s_{n} (z)$ : for…

math.CO2023

Power-Partible Reduction and Congruences for Apéry Numbers

Rong-Hua Wang, Michael X. X. Zhong

In this paper, we introduce the power-partible reduction for holonomic (or, P-recursive) sequences and apply it to obtain a series of congruences for Apéry numbers $A_{k}$ . In partic…

math.CO2022

Polynomial reduction for holonomic sequences and applications in $π$ -series and congruences

Rong-Hua Wang, Michael X. X. Zhong

Polynomial reduction, designed first for hypergeometric terms, can be used to automatically prove and generate new hypergeometric identities from old ones. In this paper, we extend…

math.CO2022

$q$ -Rational Reduction and $q$ -Analogues of Series for $π$

Rong-Hua Wang, Michael X. X. Zhong

In this paper, we present a $q$ -analogue of the polynomial reduction which was originally developed for hypergeometric terms. Using the $q$ -Gosper representation, we describe the s…

math.CO2020

Congruences Related to Dual Sequences and Catalan Numbers

Rong-Hua Wang, Michael X. X. Zhong

During the study of dual sequences, Sun introduced the polynomials \[ D_n(x,y)=\sum_{k=0}^{n}{n\choose k}{x\choose k}y^k\text{ and } S_n(x,y)=\sum_{k=0}^{n}\binom{n}{k}\binom{x}{k}…

math.CO2017

Proof of a conjecture of Morales-Pak-Panova on reverse plane partitions

Peter L. Guo, C. D. Zhao, Michael X. X. Zhong

Using equivariant cohomology theory, Naruse obtained a hook length formula for the number of standard Young tableaux of skew shape $λ / μ$ . Morales, Pak and Panova found two $q$ -anal…

math.CO2014★ 2 cited

On the Enumeration of $(s, s + 1, s + 2)$ -Core Partitions

Jane Y. X. Yang, Michael X. X. Zhong, Robin D. P. Zhou

Anderson established a connection between core partitions and order ideals of certain posets by mapping a partition to its $β$ -set. In this paper, we give a characterization of the…

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…

Polynomial reduction for q-holonomic sequences

Congruences for sums of Delannoy numbers and polynomials

Power-partible Reduction and Congruences for Schröder Polynomials

Power-Partible Reduction and Congruences for Apéry Numbers

Polynomial reduction for holonomic sequences and applications in π-series and congruences

q-Rational Reduction and q-Analogues of Series for π

Congruences Related to Dual Sequences and Catalan Numbers

Proof of a conjecture of Morales-Pak-Panova on reverse plane partitions

On the Enumeration of (s,s+1,s+2)-Core Partitions

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

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

Polynomial reduction for $q$ -holonomic sequences

Polynomial reduction for holonomic sequences and applications in $π$ -series and congruences

$q$ -Rational Reduction and $q$ -Analogues of Series for $π$

On the Enumeration of $(s, s + 1, s + 2)$ -Core Partitions