Partial Skew Dyck Paths: A Kernel Method Approach - Prodinger, Helmut (Graphs and combinatorics, 2022)
Skew Dyck paths are a variation of Dyck paths, where additionally to steps (1, 1) and ( 1 , - 1 ) a south–west step ( - 1 , - 1 ) is also allowed, provided that the path does not intersect itself. Replacing the south–west step by a red south–east step, we end up with decorated Dyck paths. We analyze partial versions of them where the path ends on a fixed level j , not necessarily at level 0. We exclusively use generating functions and derive them with the celebrated kernel method.