Speaker:  Gleb Koshevoy (CIEM RAS, Moscow)

Date and time: 8.06.2022, 17:00 (GMT +03:00)

Title: On Manin-Schechtman orders related to directed graphs

Abstract: Studying higher simplex equations (Zamolodchikov equations), in 1989 Manin and Schechtman introduced the notion of a higher Bruhat order on the $d$-element subsets of a set $[n]=\{1,2,\ldots,n\}$. Among other results in this field, they proved that the set of such orders for $n,d$ fixed, endowed with natural local transformations, constitutes a poset with one minimal and one maximal elements.

I will report on a wider model, involving the so-called convex order on certain path systems in an acyclic directed graph.

We introduce local transformations, or flips, on such orders and prove that the resulting structure gives a poset with one minimal and one maximal elements as well, and get relations between convex orders in neighboring dimensions, yielding a generalization of the above-mentioned classical results. This is  a joint work with V. Danilov and A. Karzanov.

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