Pattern-avoiding Dyck paths
Abstrak
We introduce the notion of $\textit{pattern}$ in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck paths, which we call the $\textit{Dyck pattern poset}$. Given a Dyck path $P$, we determine a formula for the number of Dyck paths covered by $P$, as well as for the number of Dyck paths covering $P$. We then address some typical pattern-avoidance issues, enumerating some classes of pattern-avoiding Dyck paths. Finally, we offer a conjecture concerning the asymptotic behavior of the sequence counting Dyck paths avoiding a generic pattern and we pose a series of open problems regarding the structure of the Dyck pattern poset.
Topik & Kata Kunci
Penulis (4)
Antonio Bernini
Luca Ferrari
Renzo Pinzani
Julian West
Akses Cepat
- Tahun Terbit
- 2013
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2334
- Akses
- Open Access ✓