Sum sequences modulo n

被引：0

作者：

Chung, Fan ^{[1
]}

Folkman, Jon ^{[1
]}

Graham, Ron ^{[1
]}

机构：

[1] Univ Calif San Diego, San Diego, CA 92103 USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2018年 / 158卷

关键词：

Sequences; Uniform distribution; CYCLIC DIFFERENCE SETS; PERFECT ADDITION SETS;

D O I：

10.1016/j.jcta.2018.03.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A sum sequence modulo n is a sequence S = (s(1), s(2), . . . , s(d)) of elements in Z/nZ such that every x is an element of Z/nZ can be represented as s(i)+s(j), i < j, in the same number lambda of ways. For example, (0,1, 2, 4) is a sum sequence modulo 6 with lambda = 1. We examine polynomials associated with sum sequences using tools from number theory, combinatorics and Galois theory. In particular, we give a complete characterization of sum sequences and their associated polynomials. We also describe some variations on these ideas and mention several possible generalizations to arbitrary finite groups. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：290 / 314

页数：25

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