Inequalities for the number of $t$-hooks in two partition classes arising from sum-product identities

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Aritram Dhar, Byungchan Kim, Eunmi Kim, Ae Ja Yee
DOI: 10.48550/arxiv.2603.01112
Cited by: 0
References: 2

Abstract

Motivated by recent study on the number of $t$-hooks in partitions arising from Euler's partition identity, we investigate the number of $t$-hooks in the sets from the first Rogers-Ramanujan identity and the first little Göllitz identity. In particular, for $t=1,2$, we obtain the generating functions for the number of $t$-hooks and prove $t$-hook inequalities by deriving asymptotic formulas.

Fields of Study & Subjects

Advanced Mathematical Identities Advanced Combinatorial Mathematics Analytic Number Theory Research

Publication details

Journal / source
arXiv (Cornell University)
Publication date
1 March 2026
Language
EN
Document type
Preprint