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The Existence of (2n-4,2n-1)-extended m-near-Skolem Sequences(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2023年03期
Page:
1-5
Research Field:
数学
Publishing date:

Info

Title:
The Existence of (2n-4,2n-1)-extended m-near-Skolem Sequences
Author(s):
Wang Yanle1; Cao Haitao2
(1.Honor College,Nanjing Normal University,Nanjing 210023,China)
(2.School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China)
Keywords:
Skolem sequence;  Langford sequence;  (p; q)-extended m-near-Skolem sequence
PACS:
O157.2
DOI:
10.3969/j.issn.1001-4616.2023.03.001
Abstract:
Let n be a positive integer,m∈{1,2,…,n},p,q∈{1,2,…,2n},p<q. A(p,q)-extended m-near-Skolem sequence of order n is a sequence S=(s1,s2,…,s2n)with elements in M={0,1,2,…,n}\{m},which satisfies the following property:(1)sp=sq=0;(2)for every positive interger k∈M,there are exactly two integers i,j,1≤i<j≤2n,such that si=sj=k and j-i=k. In this paper,we prove that the necessary conditions for the existence of (2n-4,2n-1)-extended m-near-Skolem sequences are also sufficient by sequence appending method and direct construction method.

References:

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Last Update: 2023-09-15