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math.CO2026
Proofs of two conjectures of Berkovich and Dhar on hook lengths
Rong Chen
We prove stronger forms of two conjectures of Berkovich and Dhar concerning a coefficientwise inequality and pairs of hooks of length two in bounded partitions. The coefficientwise…
math.CO2026
Two-colored generalized Frobenius partitions and minimal-excludant sums over bipartitions
Rong Chen, Kang-Yu Wang, Yi-ning Wang
Let $\cpsi_{2,a}(n)$ denote the number of -colored Frobenius partitions of weight , where the two rows have prescribed length difference. We study the two cases and…
math.NT2026
A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture
Rong Chen, Tianjian Xu
In this paper, we prove a generalization of a conjecture of Amdeberhan, Andrews, and Ballantine on double Lambert series. Motivated by a question raised by Cui, Kumar, and Singh co…