Very odd sequences
type: Item
instance of: scholarly article
title: Very odd sequences
zbMATH Open document ID: 0827.11014
DOI: 10.1016/0097-3165(95)90017-9
author: Nicholas F. J. Inglis
author: Julian D. A. Wiseman
published in: Journal of Combinatorial Theory. Series A
publication date: 1995-12-11T00:00:00Z
review text: About 20 years ago, J. Pelikán made the following conjecture. Let \(a_0, a_1, \dots, a_{n-1}\) be a binary sequence of length \(n\), and let \(A_k= \sum_{i=0}^{n-k-1} a_i a_{i+k}\), \(0\leq k\leq n\); then, for \(n\geq 5\), some \(A_k\) is even. The present authors show that this conjecture is false, determining precisely those values of \(n\) for which it fails. However, it seems that this result was obtained earlier by \textit{F. J. MacWilliams} and \textit{A. M. Odlyzko} in a 1977 paper which appeared in the same journal [J. Comb. Theory, Ser. A 22, 110-114 (1977; Zbl 0345.12010)].
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 774646
zbMATH Keywords: Pelikán's conjecture
zbMATH Keywords: binary sequence
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90017-9
OpenAlex ID: W2034387326
cites work: On a conjecture of J. Pelikán
cites work: Q3856819
cites work: Q5733527
cites work: Q3496299
cites work: Q5690468
Recommended article: A generalization of very odd sequences
Recommended article: Unusual Prime Number Sequences
Recommended article: Q3152851
Recommended article: Q3052984
Recommended article: Q3060414
Recommended article: A remarkable sequence of integers
Recommended article: Stanley sequences with odd character
Recommended article: A remarkable Lenakel sequence
description: scientific article; zbMATH DE number 774646