Research Article

Interior vertices and edges in integer partitions

Published in: Quaestiones Mathematicae
Volume 48 , issue 4 , 2025 , pages: 623–637

DOI: 10.2989/16073606.2024.2411628

Author(s): Aubrey Blecher University of the Witwatersrand, South Africa , Charlotte Brennan University of the Witwatersrand, South Africa , Arnold Knopfmacher University of the Witwatersrand, South Africa , Toufik Mansour University of Haifa, Israel

Keywords: Primary: Primary: 05A15 , Secondary: Secondary: 05A05 , Partitions , vertices , edges , generating function , asymptotics

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Abstract

This paper characterises the shape of the Young diagram associated with integer partitions in terms of two newly invented statistics which are defined in the text: namely interior vertices and horizontal edges. Generating functions and associated asymptotic results are developed for both interior vertices and horizontal edges.

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