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arXiv · 1603.01422

Short note on the number of 1-ascents in dispersed dyck paths

Kairi Kangro·Mozhgan Pourmoradnasseri·Dirk Oliver Theis
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Abstract

A dispersed Dyck path (DDP) of length n is a lattice path on $N\times N$ from (0,0) to (n,0) in which the following steps are allowed: "up" (x, y) $\to$ (x+1, y+1); "down" (x, y) $\to$ (x+1, y-1); and "right" (x,0) $\to$ (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.

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Kairi Kangro, Mozhgan Pourmoradnasseri, Dirk Oliver Theis. 2016-03-04. Short note on the number of 1-ascents in dispersed dyck paths. https://arxiv.org/abs/1603.01422

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