Lower bounds and exact values of the 2-color off-diagonal generalized weak Schur numbers WS(2;k1,k2) (Brief Announcement).

In this study, we focus on the concept of the 2-color off-diagonal generalized weak Schur numbers, denoted as WS(2; k 1 , k 2). These numbers are defined for integers k i ≥ 2, where i = 1 , 2, as the smallest integer M , such that any 2-coloring of the integer interval [1, M ] must contain a 2-colored solution to the equation E kj : x 1 + x 2 +... + x kj = x kj + 1 for j = 1,2, with the condition that x i ≠ x j when i ≠ j. Our objective is to determine lower bounds for these 2-color off-diagonal generalized weak Schur numbers and demonstrate that in several cases, these lower bounds match the exact values. [ABSTRACT FROM AUTHOR]