Research Article

Interior vertices and edges in integer partitions

Published in: Quaestiones Mathematicae
Volume 48 , issue 4 : Entrepreneurship and Africa’s Cultural Context , 2024 , 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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