Abstract:Dyck paths and certain black/white labelling of nodes leads to the \emph{white-height}. Using generating functions and tricks of the trade, we establish that the average white-height among Dyck paths of half length $n$ is asymptotic to $\frac12\sqrt{\pi n}$ for two different models. These are appealing results that could be presented to students to learn the trade. A last section links walks with double steps and 2-Motzkin paths. For them, the white-height is the natural concept.
Folks who might be offended by the notion of \emph{white-height} might choose their own colours that they like.
From: Helmut Prodinger [view email]
[v1]
Mon, 8 Jun 2026 18:11:58 UTC (8 KB)
[v2]
Sat, 13 Jun 2026 21:09:43 UTC (10 KB)
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