Interior vertices and edges in integer partitions

Aubrey Blecher; Charlotte Brennan; Arnold Knopfmacher; Toufik Mansour

doi:10.2989/16073606.2024.2411628

Interior vertices and edges in integer partitions

Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour

Department of Mathematics

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

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.

Original language	English
Pages (from-to)	623-637
Number of pages	15
Journal	Quaestiones Mathematicae
Volume	48
Issue number	4
DOIs	https://doi.org/10.2989/16073606.2024.2411628
State	Published - 2025

Bibliographical note

Publisher Copyright:
© 2024 The Author(s). Co-published by NISC Pty (Ltd) and Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Partitions
asymptotics
edges
generating function
vertices

ASJC Scopus subject areas

Mathematics (miscellaneous)

Access to Document

10.2989/16073606.2024.2411628

Cite this

@article{262dccf017f6401ab46ad5b4a6a9ba62,

title = "Interior vertices and edges in integer partitions",

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.",

keywords = "Partitions, asymptotics, edges, generating function, vertices",

author = "Aubrey Blecher and Charlotte Brennan and Arnold Knopfmacher and Toufik Mansour",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s). Co-published by NISC Pty (Ltd) and Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2025",

doi = "10.2989/16073606.2024.2411628",

language = "English",

volume = "48",

pages = "623--637",

journal = "Quaestiones Mathematicae",

issn = "1607-3606",

publisher = "Taylor and Francis",

number = "4",

}

TY - JOUR

T1 - Interior vertices and edges in integer partitions

AU - Blecher, Aubrey

AU - Brennan, Charlotte

AU - Knopfmacher, Arnold

AU - Mansour, Toufik

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Partitions

KW - asymptotics

KW - edges

KW - generating function

KW - vertices

UR - https://www.scopus.com/pages/publications/85208265348

U2 - 10.2989/16073606.2024.2411628

DO - 10.2989/16073606.2024.2411628

M3 - Article

AN - SCOPUS:85208265348

SN - 1607-3606

VL - 48

SP - 623

EP - 637

JO - Quaestiones Mathematicae

JF - Quaestiones Mathematicae

IS - 4

ER -

Interior vertices and edges in integer partitions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this