Asymptotics and inequalities for the distinct partition function
Combinatorics
2025-12-25 v1 Number Theory
Abstract
In this paper, we give explicit error bounds for the asymptotic expansion of the shifted distinct partition function for any nonnegative integer . Then based on this refined asymptotic formula, we give the exact thresholds of for the inequalities derived from the invariants of the quartic binary form, the double Tur\'{a}n inequalities, the Laguerre inequalities and their corresponding companion versions.
Cite
@article{arxiv.2512.21205,
title = {Asymptotics and inequalities for the distinct partition function},
author = {Gargi Mukherjee and Helen W. J. Zhang and Ying Zhong},
journal= {arXiv preprint arXiv:2512.21205},
year = {2025}
}
Comments
22 pages