### Abstract

An (n,k)-sequence has been studied. A permutation a_{1},a_{2},...,a_{kn} of 0,1,...,kn-1 is an (n,k)-sequence if a_{s+d}-a_{s}≢a_{t+d}-a_{t}(modn) whenever ⌊a_{s+d}/n⌋=⌊a_{s}/n⌋ and ⌊a_{t+d}/n⌋=⌊a_{t}/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 language | English |
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Pages (from-to) | 183-192 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 105 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2000 Oct 15 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*105*(1-3), 183-192. https://doi.org/10.1016/S0166-218X(00)00183-9