Bijections for faces of braid-type arrangements
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915178750148608 |
|---|---|
| author | Bernardi, Olivier |
| author_facet | Bernardi, Olivier |
| contents | We establish a general bijective framework for encoding faces of some classical hyperplane arrangements.
Precisely, we consider hyperplane arrangements in $\mathbb{R}^n$ whose hyperplanes are all of the form $\{x_i-x_j=s\}$ for some $i,j\in[n]$ and $s\in \mathbb{Z}$. Such an arrangement $A$ is \emph{strongly transitive} if it satisfies the following condition: if $\{x_i-x_j=s\}\notin A$ and $\{x_j-x_k=t\}\notin A$ for some $i,j,k\in [n]$ and $s,t\geq 0$, then $\{x_i-x_k=s+t\}\notin A$.
For any strongly transitive arrangement $A$, we establish a bijection between the faces of $A$ and some set of decorated plane trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bijections for faces of braid-type arrangements Bernardi, Olivier Combinatorics We establish a general bijective framework for encoding faces of some classical hyperplane arrangements. Precisely, we consider hyperplane arrangements in $\mathbb{R}^n$ whose hyperplanes are all of the form $\{x_i-x_j=s\}$ for some $i,j\in[n]$ and $s\in \mathbb{Z}$. Such an arrangement $A$ is \emph{strongly transitive} if it satisfies the following condition: if $\{x_i-x_j=s\}\notin A$ and $\{x_j-x_k=t\}\notin A$ for some $i,j,k\in [n]$ and $s,t\geq 0$, then $\{x_i-x_k=s+t\}\notin A$. For any strongly transitive arrangement $A$, we establish a bijection between the faces of $A$ and some set of decorated plane trees. |
| title | Bijections for faces of braid-type arrangements |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.00662 |