Tropical geometry is sensitive to embeddings of algebraic varieties inside toric varieties. The purpose of this paper is to advertise tropical modifications as a tool to locally r...
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 i...
Let C(n) denote the maximum number of induced copies of C5 in graphs on n vertices. For n large enough, we show that C(n) = a · b · c · d · e + C(a) + C(b) + C(c) + C(d) + C(e...