Skew Dyck Paths Having no Peaks at Level 1
Department of Mathematical Sciences
(National Institute for Theoretical and Computational Sciences)
Skew Dyck paths are a variation of Dyck paths, where in addition to the
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.
of the On-Line Encyclopedia of Integer
(OEIS) considers such paths where peaks at level 1 are
forbidden. We provide a thorough analysis of a more general scenario,
namely partial decorated Dyck paths, ending on a prescribed level j
both from left-to-right and from right-to-left (decorated Dyck paths are
not symmetric). The approach is completely based on generating functions.
Full version: pdf,
(Concerned with sequences
Received January 3 2022; revised version received
January 17 2022.
Published in Journal of Integer Sequences,
January 26 2022.
Journal of Integer Sequences home page