Returns, Hills, and t-ary Trees
Helmut Prodinger
Department of Mathematical Sciences
Stellenbosch University
7602 Stellenbosch
South Africa
Abstract:
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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