[1]王彦乐,曹海涛.(2n-4,2n-1)-扩充m-准Skolem序列的构造[J].南京师大学报(自然科学版),2023,46(03):1-5.[doi:10.3969/j.issn.1001-4616.2023.03.001]
　Wang Yanle,Cao Haitao.The Existence of (2n-4,2n-1)-extended m-near-Skolem Sequences[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(03):1-5.[doi:10.3969/j.issn.1001-4616.2023.03.001]
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(2n-4,2n-1)-扩充m-准Skolem序列的构造()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第46卷
期数:
2023年03期
页码:
1-5
栏目:
数学
出版日期:
2023-09-15

文章信息/Info

Title:
The Existence of (2n-4,2n-1)-extended m-near-Skolem Sequences
文章编号:
1001-4616(2023)03-0001-05
作者:
王彦乐1; 曹海涛2
(1.南京师范大学强化培养学院,江苏 南京 210023)
(2.南京师范大学数学科学学院,江苏 南京 210023)
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)
关键词:
Skolem序列; Langford序列; (p; q)-扩充m-准Skolem序列
Keywords:
Skolem sequence;  Langford sequence;  (p; q)-extended m-near-Skolem sequence
分类号:
O157.2
DOI:
10.3969/j.issn.1001-4616.2023.03.001
文献标志码:
A
摘要:
设n为正整数,m∈{1,2,…,n},p,q∈{1,2,…,2n},p<q. n 阶(p,q)-扩充m-准Skolem序列是一个由集合 M={0,1,2,…,n}\{m}中元素组成的序列 S=(s1,s2,…,s2n),满足性质:(1)sp=sq=0;(2)对任意正整数 k∈M,恰好存在两个正整数 i,j,1≤i<j≤2n,使得 si=sj=k,且 j-i=k. 本文用序列拼接和直接构造等方法证明(2n-4,2n-1)-扩充m-准 Skolem序列存在的必要条件也是充分的.
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.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2023-01-19.
基金项目:国家自然科学基金项目(12071226、11931006)、江苏省大学生创新创业项目(202210319025Z).
通讯作者:曹海涛,博士,教授,博士生导师. 研究方向:组合数学. E-mail:05313@njnu.edu.cn
更新日期/Last Update: 2023-09-15