On Generalized Schur Numbers

Let L(t) represent the equation x1 + x2 + · · · + xt−1 = xt. For k 1, 0 i k − 1, and ti 3, the generalized Schur number S(k; t0, t1, . . . , tk−1) is the least positive integer m such that for every k-colouring of {1, 2, . . . , m}, there exists an i ∈ {0, 1, . . . , k − 1} such that there exists a solution to L(ti) that is monochromatic in colour i. In this paper, we report twenty-six previously unknown values of S(k; t0, t1, . . . , tk−1) and conjecture that for 4 t0 t1 t2,

• Type: Journal
• Year: 2016
• Where: EM
• Authors: Tanbir Ahmed, Daniel Schaal
• Keywords: EM 2016, Management