Some parity results for 16-cores
type: Item
instance of: scholarly article
title: Some parity results for 16-cores
zbMATH Open document ID: 0933.11048
DOI: 10.1023/A:1009879303577
author: Michael D. Hirschhorn
author: James A. Sellers
published in: The Ramanujan Journal
publication date: 2000-03-27T00:00:00Z
review text: A partition is said to be a \(t\)-core if its Ferrers graph does not contain a hook whose length is a multiple of \(t\). Let \(a_t(n)\) denote the number of \(t\)-cores of \(n\) and \((q)_\infty = \prod_{n\geq 1}(1-q^n).\) Using an identity discovered by F. G. Garvan, D. Kim and D. Stanton, namely, \[ \sum_{n\geq 0} a_t(n) q^n = \dfrac{(q^t)_\infty^t}{(q)_\infty}, \] the authors show that for \(\lambda\geq 1\) and \(n\geq 0\), \[ a_{16}\left(6561^\lambda n +\dfrac{7\cdot 6561^\lambda -255}{24}\right) \quad\text{and}\quad a_{16}\left(6561^\lambda n +\dfrac{23\cdot 6561^\lambda -255}{24}\right) \] are even.
reviewed by: Heng Huat Chan
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 1371465
zbMATH Keywords: \(t\)-cores
zbMATH Keywords: parity
MaRDI profile type: Publication
full work available at URL: a:1009879303577
OpenAlex ID: W2106238569
description: scientific article; zbMATH DE number 1371465