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Extended near Skolem sequences Part II
Journal of Combinatorial Designs ( IF 0.7 ) Pub Date : 2021-09-15 , DOI: 10.1002/jcd.21805
Catharine A. Baker 1 , Vaclav Linek 2 , Nabil Shalaby 3
Affiliation  

A k-extended q-near Skolem sequence of order n, denoted by N n q ( k ) , is a sequence s 1 , s 2 , , s 2 n 1 where s k = 0 and for each integer [ 1 , n ] \ { q } there are two indices i , j such that s i = s j = and i j = . For a N n q ( k ) to exist it is necessary that q k ( mod 2 ) when n 0 , 1 ( mod 4 ) and q k ( mod 2 ) when n 2 , 3 ( mod 4 ) , where ( n , q , k ) ( 3 , 2 , 3 ) , ( 4 , 2 , 4 ) . Any triple ( n , q , k ) satisfying these conditions is called admissible. In this article, which is Part II of three articles, we construct sequences N n q ( k ) for all admissible ( n , q , k ) with q [ n 2 , n ] .

中文翻译:

扩展近 Skolem 序列第二部分

一种 -扩展 q-near Skolem 顺序序列 n,表示为 N n q ( ) , 是一个序列 1 , 2 , , 2 n - 1 在哪里 = 0 并且对于每个整数 [ 1 , n ] \ { q } 有两个索引 一世 , j 以至于 一世 = j = 一世 - j = . 为一个 N n q ( ) 存在是必要的 q ( 模组 2 ) 什么时候 n 0 , 1 ( 模组 4 ) q ( 模组 2 ) 什么时候 n 2 , 3 ( 模组 4 ) , 在哪里 ( n , q , ) ( 3 , 2 , 3 ) , ( 4 , 2 , 4 ) . 任意三重 ( n , q , ) 满足这些条件称为可容许。在本文中,这是三篇文章的第二部分,我们构建序列 N n q ( ) 对于所有可接受的 ( n , q , ) q [ n 2 , n ] .
更新日期:2021-10-15
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