On the generating functions for partitions with repeated smallest part

George E. Andrews; Mohamed El Bachraoui

doi:10.1016/j.jmaa.2025.129537

On the generating functions for partitions with repeated smallest part

George E. Andrews
, Mohamed El Bachraoui

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider the number of integer partitions whose smallest part is repeated exactly k times and the remaining parts are not repeated. We prove that their generating functions are linear combinations of the q-Pochhammer symbols with polynomials as coefficients. Focusing on the cases k=1,2, and 3, we derive new identities and inequalities for the partitions into distinct parts.

Original language	English
Article number	129537
Journal	Journal of Mathematical Analysis and Applications
Volume	549
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2025.129537
Publication status	Published - Sept 1 2025

Keywords

Integer partitions
q-series

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2025.129537

Cite this

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abstract = "We consider the number of integer partitions whose smallest part is repeated exactly k times and the remaining parts are not repeated. We prove that their generating functions are linear combinations of the q-Pochhammer symbols with polynomials as coefficients. Focusing on the cases k=1,2, and 3, we derive new identities and inequalities for the partitions into distinct parts.",

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AB - We consider the number of integer partitions whose smallest part is repeated exactly k times and the remaining parts are not repeated. We prove that their generating functions are linear combinations of the q-Pochhammer symbols with polynomials as coefficients. Focusing on the cases k=1,2, and 3, we derive new identities and inequalities for the partitions into distinct parts.

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KW - q-series

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On the generating functions for partitions with repeated smallest part

Abstract

Keywords

ASJC Scopus subject areas

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