Author

Guoce Xin

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Preprint Jul 2026

The Ehrhart series of magic squares of orders seven and eight

Let $\mathrm{IMS}_n(m)$ 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 Ehrhart series $F_n(q)=\sum_{m\geq0}\mathrm{IMS}_n(m)q^m$ as reduced rational functions for $n=7$ and $n=8$. Their numerator--denominator degrees...

Dun Qiu, Guoce Xin, Zi-Hao Zhang · 0 citations

Preprint Aug 2026

Polynomial-Time Lattice-Point Counting without Barvinok Decomposition

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 decomposition. The algorithm instead operates directly on a rational generating function in the form of a nested root average, as produced by the...

Guoce Xin, Zi-Hao Zhang · 0 citations

Preprint Jul 2026

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

This work investigates the corresponding challenging denumerant problem and presents a polynomial-time algorithm that eliminates the computational bottlenecks caused by large values of $M$, $N$ and $b$.

Jinlong Tang, Guoce Xin, Zi-Hao Zhang · 1 citation