On the existence of rainbow 4-term arithmetic progressions

被引：6

作者：

Conlon, David

Jungic, Veselin

Radoicic, Rados

机构：

[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB2 1SB, England

[2] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

[3] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[4] CUNY, Baruch Coll, New York, NY 10010 USA

来源：

GRAPHS AND COMBINATORICS | 2007年 / 23卷 / 03期

关键词：

Arithmetic Progression; Distinct Color; Color Class; Acta Arith; Consecutive Integer;

D O I：

10.1007/s00373-007-0723-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For infinitely many natural numbers n, we construct 4-colorings of [n] = {1, 2, ..., n}, with equinumerous color classes, that contain no 4-term arithmetic progression whose elements are colored in distinct colors. This result solves an open problem of Jungic et al. (Comb Probab Comput 12:599-620, 2003) Axenovich and Fon-der-Flaass (Electron J Comb 11:R1, 2004).

引用

页码：249 / 254

页数：6

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