On (n,k)-sequences

Hong Yeop Song, June Bok Lee

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

An (n,k)-sequence has been studied. A permutation a1,a2,...,akn of 0,1,...,kn-1 is an (n,k)-sequence if as+d-as≢at+d-at(modn) whenever ⌊as+d/n⌋=⌊as/n⌋ and ⌊at+d/n⌋=⌊at/n⌋ for every s,t and d with 1≤s<t<t+d≤kn, where ⌊x⌋ is the integer part of x. We recall the "prime construction" of an (n,k)-sequence using a primitive root modulo p whenever kn+1=p is an odd prime. In this paper we show that (n,k)-sequences from the prime construction for a given p are "essentially the same" with each other regardless of the choice of primitive roots modulo p. Further, we study some interesting properties of (n,k)-sequences, especially those from prime construction. Finally, we present an updated table of essentially distinct (n,2)-sequences for n≤13. The smallest n for which the existence of an (n,2)-sequences is open now becomes 16.

Original languageEnglish
Pages (from-to)183-192
Number of pages10
JournalDiscrete Applied Mathematics
Volume105
Issue number1-3
DOIs
Publication statusPublished - 2000 Oct 15

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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