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arXiv · 2512.21205

Asymptotics and inequalities for the distinct partition function

Gargi Mukherjee·Helen W. J. Zhang·Ying Zhong
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Abstract

In this paper, we give explicit error bounds for the asymptotic expansion of the shifted distinct partition function $q(n +s)$ for any nonnegative integer $s$. Then based on this refined asymptotic formula, we give the exact thresholds of $n$ for the inequalities derived from the invariants of the quartic binary form, the double Turán inequalities, the Laguerre inequalities and their corresponding companion versions.

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Gargi Mukherjee, Helen W. J. Zhang, Ying Zhong. 2025-12-24. Asymptotics and inequalities for the distinct partition function. https://arxiv.org/abs/2512.21205

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