Intervals in Dyck paths and the wreath conjecture
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910800978903040 |
|---|---|
| author | Petr, Jan Turek, Pavel |
| author_facet | Petr, Jan Turek, Pavel |
| contents | Let $ι_{k}(m,l)$ denote the total number of intervals of length $m$ across all Dyck paths of semilength $k$ such that each interval contains precisely $l$ falls. We give the formula for $ι_{k}(m,l)$ and show that $ι_{k}(k,l)=\binom{k}{l}^2$. Motivated by this, we propose two stronger variants of the wreath conjecture due to Baranyai for $n=2k+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intervals in Dyck paths and the wreath conjecture Petr, Jan Turek, Pavel Combinatorics Let $ι_{k}(m,l)$ denote the total number of intervals of length $m$ across all Dyck paths of semilength $k$ such that each interval contains precisely $l$ falls. We give the formula for $ι_{k}(m,l)$ and show that $ι_{k}(k,l)=\binom{k}{l}^2$. Motivated by this, we propose two stronger variants of the wreath conjecture due to Baranyai for $n=2k+1$. |
| title | Intervals in Dyck paths and the wreath conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.07277 |