# 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…

## One Citation

Lattice walks ending on a coordinate hyperplane avoiding backtracking and repeats

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We work with lattice walks in Z using step set {±1} that finish with xr+1 = 0. We further impose conditions of avoiding backtracking (i.e. [v,−v]) and avoiding consecutive steps (i.e. [v, v]) each…

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