2022/03/14 by В. И. Данилов, Danilov, Vladimir I., Alexander V. Karzanov +3
Mathematics · #05B45 #05E10 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2203.06919
openalex publication_date 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As a generalization of weak Bruhat orders on permutations, 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\. 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. In this paper 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 prove that the resulting structure gives a poset with one minimal and one maximal elements as well, yielding a generalization of the above-mentioned classical result.