Periodicities of partition functions and Stirling numbers modulo \(p\)
type: Item
instance of: scholarly article
title: Periodicities of partition functions and Stirling numbers modulo \(p\)
zbMATH Open document ID: 0607.10010
DOI: 10.1016/0022-314X(87)90034-5
author: Albert Nijenhuis
author: Herbert S. Wilf
published in: Journal of Number Theory
publication date: 1987-01-01T00:00:00Z
review text: Let \(p(n,k)\) be the number of partitions of \(n\) into parts \(\leq k\), then the sequence \(\{p(j,k)\}^{\infty}_{j=k}\) is periodic modulo a prime \(p\). The authors obtain the minimum period \(Q(k,p)\) of this sequence and more generally the minimum period modulo \(p\) of \(\{p(n,T)\}\), the number of partitions of \(n\) whose parts lie in a fixed set \(T\) of positive integers. The minimum period modulo \(p\) of \(\{S(n,k)\}^{\infty}_{n=k}\), the sequence of Stirling numbers of the second kind, is also derived. The method uses cyclotomic polynomials over \(\mathbb Z_ p[x]\).
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 3981253
zbMATH Keywords: partition functions
zbMATH Keywords: periodicities modulo p
zbMATH Keywords: minimum period
zbMATH Keywords: Stirling numbers
zbMATH Keywords: cyclotomic polynomials
MaRDI profile type: Publication
cites work: The Arithmetic of Bell and Stirling Numbers
cites work: Algebraic coding theory
description: scientific article; zbMATH DE number 3981253