• Corpus ID: 221819453

Enumerating Restricted Dyck Paths with Context-Free Grammars.

@article{Bu2020EnumeratingRD,
  title={Enumerating Restricted Dyck Paths with Context-Free Grammars.},
  author={AJ Bu and Robert Dougherty-Bliss},
  journal={arXiv: Combinatorics},
  year={2020}
}
The number of Dyck paths of semilength $n$ is famously $C_n$, the $n$th Catalan number. This fact follows after noticing that every Dyck path can be uniquely parsed according to a context-free grammar. In a recent paper, Zeilberger showed that many restricted sets of Dyck paths satisfy different, more complicated grammars, and from this derived various generating function identities. We take this further, highlighting some combinatorial results about Dyck paths obtained via grammatical proof… 
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