Chen Zhang

activity

20232026

most citedThree Simple Reduction Formulas for the Denumerant Functions

3 citations · 3 across the 8 of their papers we have counts for

collaborators

9 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

A polynomial time algorithm for almost bounded denumerant

Guoce Xin, Chen Zhang, Zihao Zhang

Sylvester's denumerant $d (t; A)$ counts the number of nonnegative integer solutions to $\sum_{i = 1}^{N} a_{i} x_{i} = t$ , where $A = (a_{1}, \dots, a_{N})$ is a se…

math.CO2026

Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions

Feihu Liu, Jinlong Tang, Guoce Xin +1

For a finite sequence of positive integers $a = (a_{1}, \dots, a_{n})$ , the restricted partition function $q_{a} (k)$ denote the number of nonnegative integer solu…

math.CO2026

A proof of Xin-Zhang's tridiagonal determinant conjecture (extended version)

Jiaqiang Hu, Chen Zhang

We confirm a recent conjecture of Xin and Zhang, which establishes a simple product formula for the characteristic polynomial of an $(n - 1) \times (n - 1)$ tridiagonal matrix $C$ . Thi…

math.CO2024

Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS

Feihu Liu, Guoce Xin, Chen Zhang

In this paper, we provide an overview of Ehrhart polynomials associated with order polytopes of finite posets, a concept first introduced by Stanley. We focus on their combinatoria…

math.CO2024

A variation of the Morris constant term

Guoce Xin, Chen Zhang

The Morris constant term identity is important due to its equivalence with the well-known Selberg integral. We find a variation of the Morris constant term, denoted $h_{n} (t)$ , in th…

math.CO2024

A polynomial time algorithm for Sylvester waves when entries are bounded

Guoce Xin, Chen Zhang

The Sylvester's denumerant $ d(t; \boldsymbol{a}) $ is a quantity that counts the number of nonnegative integer solutions to the equation $ \sum_{i=1}^{N} a_i x_i = t $, where…

math.CO2024★ 3 cited

Three Simple Reduction Formulas for the Denumerant Functions

Feihu Liu, Guoce Xin, Chen Zhang

Let $A$ be a nonempty set of positive integers. The restricted partition function $p_{A} (n)$ denotes the number of partitions of $n$ with parts in $A$ . When the elements in $A$ are p…

math.CO2023

An algebraic combinatorial approach to Sylvester's denumerant

Guoce Xin, Chen Zhang

For a positive integer sequence $a = (a_{1}, \dots, a_{N + 1})$ , Sylvester's denumerant $E (a; t)$ counts the number of nonnegative integer solutions to $\sum_{i…