Paper
Skew 2-Dyck paths via the kernel method
Authors
Helmut Prodinger
Abstract
We continue on a recent concept introduced by Kariuki and Okoth, about skew 2-Dyck paths, introducing an additional down-step , together with the usual steps
(up) and down. There is the syntactical condition that and can never occur. An automaton that checks these conditions is introduced, and the
relevant generating functions are obtained by applying the kernel method to three functional equations. It is briefly discussed how the setting can be extended to -Dyck paths. As a benefit, prefixes of skew -Dyck paths are also enumerated.