The existence of near-Skolem and hooked near-Skolem sequences
type: Item
instance of: scholarly article
title: The existence of near-Skolem and hooked near-Skolem sequences
zbMATH Open document ID: 0818.05008
DOI: 10.1016/0012-365X(92)00327-N
author: Nabil Shalaby
published in: Discrete Mathematics
publication date: 1995-02-01T00:00:00Z
review text: The author has studied the near-Skolem and hooked near-Skolem sequences and it is proved that the arithmetic necessary conditions for the existence of near-Skolem and hooked near-Skolem sequences are also sufficient. These sequences are defined by the following: Let \(m\), \(n\) be integers, \(m\leq n\). A near-Skolem sequence of order \(n\), defect \(m\) is a sequence \(S= (s_ 1,s_ 2,\dots, s_{2n-2})\) of integers \(s_ i\in \{1,2,\dots, m- 1, m+1,\dots,n\}\) which satisfies the following conditions: (1) For every \(k\in \{1,2,\dots, m- 1, m+1,\dots, n\}\) there are exactly two terms \(s_ i\) and \(s_ j\) of \(S\) such that \(s_ i= s_ j= k\). (2) If \(s_ i= s_ j= k\) and \(i< j\) then \(j- i= k\). A hooked near-Skolem sequence of order \(n\), defect \(m\) is a sequence \(HS= (s_ 1, s_ 2,\dots, s_{2n- 1})\) of integers \(s_ i\in \{1,2,\dots, m-1, m+1,\dots, n\}\) which satisfies conditions (1) and (2) and \(s_{2n- 2}= 0\).
Mathematics Subject Classification ID: 05A99
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 716465
zbMATH Keywords: hooked near-Skolem sequences
zbMATH Keywords: near-Skolem sequence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 716465