On Manin-Schechtman orders related to directed graphs
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916497181376512 |
|---|---|
| author | Danilov, Vladimir I. Karzanov, Alexander V. Koshevoy, Gleb A. |
| author_facet | Danilov, Vladimir I. Karzanov, Alexander V. Koshevoy, Gleb A. |
| contents | 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 $[n]=\{1,2,\ldots,n\}$. 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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_06919 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Manin-Schechtman orders related to directed graphs Danilov, Vladimir I. Karzanov, Alexander V. Koshevoy, Gleb A. Combinatorics 05E10, 05B45 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 $[n]=\{1,2,\ldots,n\}$. 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. 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. |
| title | On Manin-Schechtman orders related to directed graphs |
| topic | Combinatorics 05E10, 05B45 |
| url | https://arxiv.org/abs/2203.06919 |