On the parity of \(p(n)\). II
type: Item
instance of: scholarly article
title: On the parity of \(p(n)\). II
zbMATH Open document ID: 0774.11060
DOI: 10.1016/0097-3165(93)90075-J
published in: Journal of Combinatorial Theory. Series A
publication date: 1993-05-16T00:00:00Z
review text: \textit{O. Kolberg} [Math. Scand. 7, 377-378 (1960; Zbl 0091.044)] has proved that \(p(n)\) is infinitely often even, infinitely often odd. In part I, the author and \textit{M. V. Subbarao} [Acta Arith. 50, 355-356 (1988; Zbl 0657.10010)] have obtained the same result for \(p(16n+r)\) for every \(r\). Congruences modulo 2 for the generating functions of \(p(3n+r)\), \(r=0,1,2\), and of \(p(5n+r)\), \(r=0,1,2,3,4\), are now used to show that for every \(r\), \(p(12n+r)\) and \(p(40n+r)\) are each infinitely often even, infinitely often odd.
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 165754
zbMATH Keywords: parity of partition function
author: Michael D. Hirschhorn
reviewed by: Betty Garrison
MaRDI profile type: Publication
cites work: Sieved Partition Functions and q-Binomial Coefficients
cites work: On the parity of p(n)
cites work: Note on the Parity of the Partition Functions.
full work available at URL: 0097-3165(93)90075-j
OpenAlex ID: W2089252042
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