From the 1 of 8 linked papers with an AI index.
8 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…
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 , the number of magic labelings with magic sum can be expressed as a sum of two polynomials in . However,…
On Ward Numbers and Increasing Schröder Trees
Elena L. Wang, Guoce Xin
The Ward numbers combinatorially enumerate set partitions with block sizes and phylogenetic trees (total partition trees). We prove that also counts \emp…
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…