On Manin–Schechtman orders related to directed graphs
Studying higher Zamolodchikov equations, in 1989 Manin and Schechtman introduced the notion of a higher Bruhat order on the d-element subsets of a set $[n] = \{1, 2, . . . , n}$. We consider a wider model, involving the so-called convex order on certain path systems in an acyclic directed graph, introduce local transformations, or flips, on such orders and establish a generalization of the Manin-Schechtman results. This is a joint work with V.Danilov and A. Karzanov.