On the regular sum-free sets

被引：4

作者：

Wen, Zhi-Xiong ^{[1
]}

Zhang, Jie-Meng ^{[1
]}

Wu, Wen ^{[2
,3
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

[3] Univ Oulu, Dept Math Sci, Oulu 90014, Finland

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2015年 / 49卷

基金：

芬兰科学院;

关键词：

D O I：

10.1016/j.ejc.2015.02.030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Cameron introduced a bijection between the set of sum-free sets and the set of all zero-one sequences. In this paper, we study the sum-free sets of natural numbers corresponding to certain zero-one sequences which contain the Cantor-like sequences and some substitution sequences, etc. Such sum-free sets considered as integer sequences are 2-regular. We also prove that sequences corresponding to certain sum-free sets are automatic. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：42 / 56

页数：15

共 13 条

[1]

Allouche J.-P., 2003, AUTOMATIC SEQUENCES, DOI DOI 10.1017/CBO9780511546563

[2] THE RING OF K-REGULAR SEQUENCES [J].

ALLOUCHE, JP ;

SHALLIT, J .

THEORETICAL COMPUTER SCIENCE, 1992, 98 (02) :163-197

[3]

Calkin Neil J., 1996, EXP MATH, V5, P131

[4]

Cameron P., 1987, Surveys in Combin, V123, P13

[5] CYCLIC AUTOMORPHISMS OF A COUNTABLE GRAPH AND RANDOM SUM-FREE SETS [J].

CAMERON, PJ .

GRAPHS AND COMBINATORICS, 1985, 1 (02) :129-135

[6] Notes on sum-free and related sets [J].

Cameron, PJ ;

Erdos, P .

COMBINATORICS PROBABILITY & COMPUTING, 1999, 8 (1-2) :95-107

[7]

CAMERON PJ, 1990, NUMBER THEORY /, P61

[8]

Catkin Neil J., 1996, MATH P CAMBRIDGE PHI, V120, P1

[9]

Catkin Neil J., 1988, THESIS U WATERLOO

[10]

Catkin Neil J., 2005, ELECT J COMBIN NUMBE, V5

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