Author

Guoce Xin

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Preprint Aug 2026

A polynomial time algorithm for almost bounded denumerant

Sylvester's denumerant $d(t; \boldsymbol{A})$ counts the number of nonnegative integer solutions to $\sum_{i=1}^{N} a_i x_i = t$, where $\boldsymbol{A} = (a_1, \dots, a_N)$ is a sequence of positive integers with $\gcd(\boldsymbol{A}) = 1$. In 2025, Xin and Zhang gave a polynomial time algorithm in $N$ for computing $d...

Guo-Ce Xin, Chen Zhang, Zi-Hao Zhang · 0 citations

Preprint Aug 2026

Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions

For a finite sequence of positive integers $\boldsymbol{a}=(a_1,\dots,a_n)$, the restricted partition function $q_{\boldsymbol{a}}(k)$ denote the number of nonnegative integer solutions to the equation $a_1x_1+a_2x_2+\cdots +a_nx_n=k$. It is proved to be a quasi-polynomial of degree $n-1$. Write $q_{\boldsymbol{a}}(k)=...

Fei-Hu Liu, Jinlong Tang, Guoce Xin et al. · 0 citations