Rainbow solutions to the Sidon equation

被引：7

作者：

Fox, Jacob ^{[1
]}

Mahdian, Mohammad ^{[2
]}

Radoicic, Rados ^{[3
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Microsoft Res Theory Grp, Redmond, WA 98052 USA

[3] CUNY, Baruch Coll, Dept Math, New York, NY 10010 USA

来源：

DISCRETE MATHEMATICS | 2008年 / 308卷 / 20期

基金：

英国科研创新办公室; 美国国家科学基金会;

关键词：

Sidon equation; rainbow solution;

D O I：

10.1016/j.disc.2007.08.071

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for every 4-coloring of (1, 2,..., n), with each color class having cardinality more than (n + 1)/6, there exists a solution of the equation x + y = z + w) with x, y, z and w belonging to different color classes. The lower bound on a color class cardinality is tight. (C) 2007 Elsevier B. V. All rights reserved.

引用

页码：4773 / 4778

页数：6

共 21 条

[1] ALEKSEEV VE, 1987, KVANT, V4, P23
[2] [Anonymous], 1987, LONDON MATH SOC LECT
[3] Axenovich M, 2004, ELECTRON J COMB, V11
[4] BALANDRAUD E, 2007, J COMBIN A IN PRESS
[5] CAMERON P, 2007, REV MAT IBE IN PRESS
[6] CONLON D, 2007, GRAPHS COMB IN PRESS
[7] Rainbow solutions of linear equations over Zp
Conlon, David
[J]. DISCRETE MATHEMATICS, 2006, 306 (17) : 2056 - 2063
[8] Graham R. L., 1990, RAMSEY THEORY
[9] Guy R. K., 1994, UNSOLVED PROBLEMS NU
[10] Rainbow arithmetic progressions and anti-Ramsey results
Jungic, V
Licht, J
Mahdian, M
Nesetril, J
Radoicic, R
[J]. COMBINATORICS PROBABILITY & COMPUTING, 2003, 12 (5-6) : 599 - 620

← 1 2 3 →