26 search results - page 1 / 6 » Independence for partition regular equations |
JCT
2007
13 years 5 months ago
2007
A matrix A is said to be partition regular (PR) over a subset S of the positive integers if whenever S is finitely coloured, there exists a vector x, with all elements in the sam...
JCT
2007
13 years 5 months ago
2007
Let G be a d-regular graph with girth g, and let α be the independence number of G. We show that α(G) ≥ 1 2 1 − (d − 1)−2/(d−2) − (g) n where (g) → 0 as g → ∞,...
RSA
2010
13 years 3 months ago
2010
We study thresholds for Ramsey properties of random discrete structures. In particular, we determine the threshold for Rado’s theorem for solutions of partition regular systems o...
JCT
2010
13 years 3 months ago
2010
A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive intege...
DM
2006
13 years 5 months ago
2006
It is easy to deduce from Ramsey's Theorem that, given positive integers a1, a2, . . . , am and a finite colouring of the set N of positive integers, there exists an injectiv...