Large p-core p'-partitions and walks on the additive residue graph

Eoghan McDowell

doi:10.48550/arXiv.2207.01824

Large p-core p'-partitions and walks on the additive residue graph

Eoghan McDowell^*

^*Corresponding author for this work

School of Mathematics

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Abstract

This paper investigates partitions which have neither parts norhook lengths divisible by p, referred to as p-core p'-partitions. We showthat the largest p-core p'-partition corresponds to the longest walk on agraph with vertices {0, 1,...,p−1} and labelled edges defined via addition modulo p. We also exhibit an explicit family of large p-core p'-partitions, giving a lower bound on the size of the largest such partition which is of the same degree as the upper bound found by McSpirit and Ono.

Original language	English
Pages (from-to)	857-871
Number of pages	25
Journal	Annals of Combinatorics
Volume	27
Issue number	4
Early online date	24 Nov 2023
DOIs	https://doi.org/10.48550/arXiv.2207.01824 https://doi.org/10.1007/s00026-022-00622-2
Publication status	Published - 1 Dec 2023

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10.1007/s00026-022-00622-2

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AB - This paper investigates partitions which have neither parts norhook lengths divisible by p, referred to as p-core p'-partitions. We showthat the largest p-core p'-partition corresponds to the longest walk on agraph with vertices {0, 1,...,p−1} and labelled edges defined via addition modulo p. We also exhibit an explicit family of large p-core p'-partitions, giving a lower bound on the size of the largest such partition which is of the same degree as the upper bound found by McSpirit and Ono.

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Large p-core p'-partitions and walks on the additive residue graph

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