Yueming Zhong

activity

20192026

collaborators

10 papers

math.CO2026

Exact Ehrhart Series of Birkhoff Polytopes via Constant Terms and Finite-Field Evaluation

Xinru Jiang, Guoce Xin, Chen Zhang +1

The Ehrhart series of the $n$ th Birkhoff polytope is $\sum_{r \geq 0} H_{n} (r) z^{r}$ , where $H_{n} (r)$ counts nonnegative integer $n \times n$ matrices whose row and column sums all equal $r…

math.CO2026

Transfer Matrices and Ehrhart Theory for Path and Cyclic Block Polytopes

Xinru Jiang, Shuai Yang, Yueming Zhong

We study block polytopes whose variables are divided into equal-size blocks and whose local inequalities bound the total contribution of adjacent blocks. For blocks arranged along…

math.CO2026

Alternating adjacent-sum polytopes: transfer matrices and Ehrhart series

Xinru Jiang, Suzhen Wen, Yueming Zhong

We study a period-two family of adjacent-sum lattice polytopes whose consecutive-coordinate bounds alternate between $s$ and $s + 1$ . This provides a simple non-uniform deformation o…

math.CO2026

Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs

Guoce Xin, Yueming Zhong, Yangbiao Zhou

Stanley's theorem establishes that for any finite graph $G$ , the number $h_{G} (s)$ of magic labelings with magic sum $s$ can be expressed as a sum of two polynomials in $s$ . However,…

math.CO2022

The constant term algebra of type $A$ : the Structure

Guoce Xin, Chen Zhang, Yue Zhou +1

In this paper, we discover a new noncommutative algebra. We refer this algebra as the constant term algebra of type $A$ , which is generated by certain constant term operators. We c…

math.CO2022

Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials

Guoce Xin, Yueming Zhong

In chemistry, Cyvin-Gutman enumerates Kekulé numbers for certain benzenoids and record it as $A 050446$ on OEIS. This number is exactly the two variable array $T (n, m)$ defined by th…

math.CO2021

A symmetric chain decomposition of $N (m, n)$ of composition

Yueming Zhong

A poset is called a symmetric chain decomposition if the poset can be expressed as a disjoint union of symmetric chains. For positive integers $m$ and $n$ , let $N (m, n)$ denote the…

math.CO2021

On Magic Distinct Labellings of Simple Graphs

Guoce Xin, Xinyu Xu, Chen Zhang +1

A magic labelling of a graph $G$ with magic sum $s$ is a labelling of the edges of $G$ by nonnegative integers such that for each vertex $v \in V$ , the sum of labels of all edges in…

math.CO2021

Constructing explicit Sperner chain decompositions for $L (3, n)$ and $L (4, n)$ via Greedy Algorithms and chain tableaux

Guoce Xin, Yueming Zhong

Let $L (m, n)$ denote Young's lattice, consisting of all partitions whose Young diagrams are contained within an $m \times n$ rectangle. It is a classical result that the partially or…

math.CO2019

On Parity Unimodality of $q$ -Catalan Polynomials

Guoce Xin, Yueming Zhong

A polynomial $A (q) = \sum_{i = 0}^{n} a_{i} q^{i}$ is said to be unimodal if $a_{0} \leq a_{1} \leq \dots \leq a_{k} \geq a_{k + 1} \geq \dots \geq a_{n}$ . We investigate the unimodality of rational $q$ -Catal…

Exact Ehrhart Series of Birkhoff Polytopes via Constant Terms and Finite-Field Evaluation

Transfer Matrices and Ehrhart Theory for Path and Cyclic Block Polytopes

Alternating adjacent-sum polytopes: transfer matrices and Ehrhart series

Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs

The constant term algebra of type A: the Structure

Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials

A symmetric chain decomposition of N(m,n) of composition

On Magic Distinct Labellings of Simple Graphs

Constructing explicit Sperner chain decompositions for L(3,n) and L(4,n) via Greedy Algorithms and chain tableaux

On Parity Unimodality of q-Catalan Polynomials

The constant term algebra of type $A$ : the Structure

A symmetric chain decomposition of $N (m, n)$ of composition

Constructing explicit Sperner chain decompositions for $L (3, n)$ and $L (4, n)$ via Greedy Algorithms and chain tableaux

On Parity Unimodality of $q$ -Catalan Polynomials