On ordered Ramsey numbers of matchings versus triangles

For graphs G^< and H^< with linearly ordered vertex sets, the ordered Ramsey number r_< (G^<, H^<) is the smallest positive integer N such that any red-blue coloring of the edges of the complete ordered graph KN^< on N vertices contains either a blue copy of G^< or a red copy of H^<. Motivated by a problem of Conlon, Fox, Lee, and Sudakov (2017), we study the numbers r_< (M^<, K3^{<) whereM <} is an ordered matching on n vertices. We prove that almost all n-vertex ordered matchings M^< with interval chromatic number 2 satisfy r_< (M^<, K3^{<)∈Ω((n/logn)5/4}) and r_< (M^<, K3^{<)∈ O(n7/4}), improving a recent result by Rohatgi (2019). We also show that there are nvertex ordered matchings M^< with interval chromatic number at least 3 satisfying r_< (M^<, K3^{<)∈Ω((n/logn)4/3}), which asymptotically matches the best known lower bound on these off-diagonal ordered Ramsey numbers for general n-vertex ordered matchings.