Guoce Xin

activity

20052026

most citedOn partitions avoiding 3-crossings

42 citations · 42 across the 9 of their papers we have counts for

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

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 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.CO2025

On Ward Numbers and Increasing Schröder Trees

Elena L. Wang, Guoce Xin

The Ward numbers $W (n, k)$ combinatorially enumerate set partitions with block sizes $\geq 2$ and phylogenetic trees (total partition trees). We prove that $W (n, k)$ also counts \emp…

math.CO2025

Closed-Form Decomposition for Simplicial Cones and PDBarv Algorithm for Lattice Point Counting

Sihao Tao, Guoce Xin, Zihao Zhang

Counting lattice points within a rational polytope is a foundational problem with applications across mathematics and computer science. A key approach is Barvinok's algorithm, whic…

math.CO2025

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle

Jinlong Tang, Guoce Xin

This paper resolves an open problem raised by Ekhad and Zeilberger for computing $ω (10000)$ , which is related to Stern's triangle. While $ν (n)$ , defined as the sum of squared coeff…

math.CO2025

A combinatorial simplicial cone decomposition

Guoce Xin, Xinyu Xu, Zihao Zhang

This paper introduces an algebraic combinatorial approach to simplicial cone decompositions, a key step in solving inhomogeneous linear Diophantine systems and counting lattice poi…

math.CO2024

A Combinatorial Decomposition of Knapsack Cones

Guoce Xin, Yingrui Zhang, Zihao Zhang

In this paper, we focus on knapsack cones, a specific type of simplicial cones that arise naturally in the context of the knapsack problem $x_{1} a_{1} + \dots + x_{n} a_{n} = a_{0}$ . We pr…

math.CO2005★ 42 cited

On partitions avoiding 3-crossings

Mireille Bousquet-Mélou, Guoce Xin

A partition on $[n]$ has a crossing if there exists $i_1 < i_2 < j_1 < j_2$ such that $i_1$ and $j_1$ are in the same block, $i_2$ and $j_2$ are in the same block, but $i_1$ and…