Partitions which are simultaneously \(t_1\)- and \(t_2\)-core
type: Item
instance of: scholarly article
title: Partitions which are simultaneously \(t_1\)- and \(t_2\)-core
zbMATH Open document ID: 1001.05015
DOI: 10.1016/S0012-365X(01)00343-0
author: Jaclyn Anderson
published in: Discrete Mathematics
publication date: 2002-05-28T00:00:00Z
review text: For any node in the Ferrers-Young diagram of a partition of an integer \(n\), define the hook number of the node to be \(1+ r+ d\) where \(r\), \(d\) are the numbers of nodes to its right, downwards respectively. A partition is \(t\)-core if none of its hook numbers is divisible by \(t\). It is shown that if \(t_1\), \(t_2\) are relatively prime then there are precisely \({1\over t_1+ t_2} {t_1+ t_2\choose t_1}\) partitions which are both \(t_1\)-core and \(t_2\)-core. If \(t_1\), \(t_2\) are not relatively prime, there are infinitely many such partitions.
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 1746262
zbMATH Keywords: partition
zbMATH Keywords: hook number
MaRDI profile type: Publication
full work available at URL: s0012-365x(01)00343-0
OpenAlex ID: W1630698243
description: scientific article; zbMATH DE number 1746262