From the 1 of 10 linked papers with an AI index.
10 papers
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…
The Ehrhart series of magic squares of orders seven and eight
Dun Qiu, Guoce Xin, Zihao Zhang
Let count the nonnegative integer matrices whose row sums, column sums, main-diagonal sum, and antidiagonal sum are all . We determine the Ehrhar…
Polynomial-Time Evaluation of Aardal-Lenstra Denumerants via Constant Term Method
Jinlong Tang, Guoce Xin, Zihao Zhang
The paper gives a polynomial‑time algorithm for counting the non‑negative integer solutions of knapsack equations with coefficients of the form a_i = p_i M + r_i N, using a constan…
An Algorithm for Computing Hankel Determinants up to Order
Feihu Liu, Guoce Xin, Zihao Zhang
Given the rational power series , the Hankel determinant of order is defined as $H_n(h(x)) := \det (h_{i+j})_{1 \leq i,j \le…
Magic Positivity for the Ehrhart Polynomials of Partial Permutohedra
Feihu Liu, Zihao Zhang
For positive integers \(m,n\), the partial permutohedron is a lattice polytope constructed as the convex hull of vectors in that have dist…
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…