Jinlong Tang

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math.CO2026

Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions

Feihu Liu, Jinlong Tang, Guoce Xin +1

For a finite sequence of positive integers $a = (a_{1}, \dots, a_{n})$ , the restricted partition function $q_{a} (k)$ denote the number of nonnegative integer solu…

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

Proofs of four generating function conjectures for arbor polytopes

Feihu Liu, Jinlong Tang

This paper proves four conjectured generating series, due to Chapoton, which concern invariants of posets and polytopes associated with a specific sequence of arbors. Two of these…

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…