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...
We prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We the...
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...
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...
In 1973, Deuber published his famous proof of Rado's conjecture regarding partition regular sets. In his proof, he invented structures called (m, p, c)-sets and gave a partit...