Zi-Hao Zhang

activity

20212026

collaborators

10 papers

math.CO2026

The Ehrhart series of magic squares of orders seven and eight

Dun Qiu, Guoce Xin, Zihao Zhang

Let $IMS_{n} (m)$ count the $n \times n$ nonnegative integer matrices whose row sums, column sums, main-diagonal sum, and antidiagonal sum are all $m$ . We determine the Ehrhar…

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

Polynomial-Time Lattice-Point Counting without Barvinok Decomposition

Guoce Xin, Zihao Zhang

By using constant term manipulations, we present the first polynomial-time algorithm for lattice-point counting in fixed dimension that does not rely on Barvinok's unimodular decom…

math.CO2026

Polynomial-Time Evaluation of Aardal-Lenstra Denumerants via Constant Term Method

Jinlong Tang, Guoce Xin, Zihao Zhang

Aardal and Lenstra systematically studied hard knapsack problems of the form $a_{1} x_{1} + \dots + a_{n} x_{n} = b$ , where $a_{i} = p_{i} M + r_{i} N$ , $(M, N)$ is a coprime pair of positive integers, and th…

math.CO2026

Magic Positivity for the Ehrhart Polynomials of Partial Permutohedra

Feihu Liu, Zihao Zhang

For positive integers $m,n$, the partial permutohedron $P (m, n)$ is a lattice polytope constructed as the convex hull of vectors in ${0, 1, \dots, n}^{m}$ that have dist…

math.CO2025

On the quantum chromatic number of Hamming and generalized Hadamard graphs

Xiwang Cao, Keqin Feng, Hexiang Huang +2

As a fundamental metric for quantifying quantum advantage in non-local games, the quantum chromatic number reveals the power of entanglement in distributed tasks. In this paper, we…