Binary partitions revisited
type: Item
instance of: scholarly article
title: Binary partitions revisited
zbMATH Open document ID: 1004.05007
author: Øystein J. Rødseth
author: James A. Sellers
published in: Journal of Combinatorial Theory. Series A
publication date: 2003-02-01T00:00:00Z
review text: The binary partition function \(b_k(n)\) counts the number of representations of \(n\) as a sum of not necessarily distinct powers of 2 strictly less than \(2^k\). The authors prove that for \(1 \leq r \leq k-2\), we have \(b_k(2^{r+2}n)-b_{k-2}(2^rn) \equiv 0 \pmod{2^{\lfloor 3r/2\rfloor+2}}. \) For \(k \geq 3\) and \(t \geq 1\), we have \(b_k(2^{k+t}n)-b_k(2^{k+t-2}n) \equiv 0 \pmod{2^{\lfloor 3k/2\rfloor+t+2}}\).
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 1760665
zbMATH Keywords: binary partition
reviewed by: David M. Bressoud
MaRDI profile type: Publication
full work available at URL: jcta.2001.3223
OpenAlex ID: W2053250743
cites work: Q4146776
cites work: Q5573494
cites work: Q5616177
cites work: A simple proof of the Churchhouse conjecture concerning binary partitions
cites work: Q4134054
cites work: Q5605902
cites work: On \(m\)-ary partition function congruences: A fresh look at a past problem
DOI: 10.1006/JCTA.2001.3223
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description: scientific article; zbMATH DE number 1760665