A set of integers is weakly sum-free if it does not contain a solution of x+y = z with x 6= y. Given n 1, the weak Schur number WS(n) is the maximal integer N such that there exists an n-coloring of the set {1, 2, . . . , N} such that each monochromatic subset is weakly sum-free. We give new lower bounds on WS(n) for n = 7, 8 and 9 by constructing highly structured n-colorings, with some computer help.
展开▼
