Journal of Integer Sequences, Vol. 19 (2016), Article 16.7.2

Returns, Hills, and t-ary Trees

Helmut Prodinger
Department of Mathematical Sciences
Stellenbosch University
7602 Stellenbosch
South Africa


A recent analysis of returns and hills of generalized Dyck paths is carried over to the language of t-ary trees, from which, by explicit bivariate generating functions, all the relevant results follow quickly and smoothly. A conjecture about the (discrete) limiting distribution of hills is settled in the affirmative.

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(Concerned with sequences A001764 A006013 A006629 A006630 A006631.)

Received June 27 2016; revised versions received August 26 2016; August 27 2016. Published in Journal of Integer Sequences, August 29 2016.

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