Summary: Sure monochromatic subset sums
Noga Alon
Paul Erd¨os
Abstract
Let f(n) denote the smallest integer f such that one can color the integers {1, 2, . . . , n - 1}
by f colors so that there is no monochromatic subset the sum of whose elements is n. It is shown
that
(
n1/3
log4/3
n
) f(n) O(
n1/3
(log log n)1/3
log1/3
n
).
The lower bound settles a problem of Erd¨os.
1 Introduction
For an integer n > 1 let f(n) denote the smallest integer f such that one can color the integers

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

Collections: Mathematics