Short note on the number of 1-ascents in dispersed dyck paths
Combinatorics
2016-03-07 v1
Abstract
A dispersed Dyck path (DDP) of length n is a lattice path on from (0,0) to (n,0) in which the following steps are allowed: "up" (x, y) (x+1, y+1); "down" (x, y) (x+1, y-1); and "right" (x,0) (x+1,0). An ascent in a DDP is an inclusion-wise maximal sequence of consecutive up steps. A 1-ascent is an ascent consisting of exactly 1 up step. We give a closed formula for the total number of 1-ascents in all dispersed Dyck paths of length n, A191386 in Sloane's OEIS. Previously, only implicit generating function relations and asymptotics were known.
Keywords
Cite
@article{arxiv.1603.01422,
title = {Short note on the number of 1-ascents in dispersed dyck paths},
author = {Kairi Kangro and Mozhgan Pourmoradnasseri and Dirk Oliver Theis},
journal= {arXiv preprint arXiv:1603.01422},
year = {2016}
}