Queries for Dyck paths: search statistic / browse statistics / browse maps from / browse maps to

Definition & Example

Equivalently, a Dyck path of semilength $n$ can be seen as

the 5 Dyck paths of size 3
  [1,0,1,0,1,0]   [1,0,1,1,0,0]   [1,1,0,0,1,0]   [1,1,0,1,0,0]   [1,1,1,0,0,0]


This yields the recurrence

$$\operatorname{Cat}(n+1) = \sum_{k=1}^n \operatorname{Cat}(k) \cdot \operatorname{Cat}(n-k).$$



Sage examples

Technical information for database usage

If you want to edit this wiki page, you can download the raw markdown and send your new version to info@findstat.org