Unique Sequences Containing No k-Term Arithmetic Progressions

被引：0

作者：

Ahmed, Tanbir ^{[1
]}

Dybizbanski, Janusz ^{[2
]}

Snevily, Hunter ^{[3
]}

机构：

[1] Concordia Univ, Dept Comp Sci & Software Engn, Montreal, PQ, Canada

[2] Univ Gdansk, Inst Informat, PL-80952 Gdansk, Poland

[3] Univ Idaho, Dept Math, Moscow, ID 83843 USA

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2013年 / 20卷 / 04期

关键词：

INTEGERS; SETS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with calculating r(k, n), the length of the longest k-Ap free subsequences in 1,2,...,n. We prove the basic inequality r(k,n) <= n - [m/2], where n = m(k - 1) + r and r < k - 1. We also discuss a generalization of a famous conjecture of Szekeres (as appears in Erdos and Turan [4]) and describe a simple greedy algorithm that appears to give an optimal k-AP free sequence infinitely often. We provide many exact values of r(k, n) in the Appendix.

引用

页数：24

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