Geodesic
Returns, hills, and \(t\)-ary trees
Journal of integer sequences, Tome 19 (2016) no. 7
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.
Classification : 05A15, 05A16, 60C05
Keywords: t-ary trees, Dyck paths, generating functions, negative binomial distribution, asymptotic tree enumeration 
@article{JIS_2016__19_7_a1,
     author = {Prodinger,  Helmut},
     title = {Returns, hills, and \(t\)-ary trees},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {7},
     zbl = {1348.05023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a1/}
}
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%J Journal of integer sequences
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Prodinger,  Helmut. Returns, hills, and \(t\)-ary trees. Journal of integer sequences, Tome 19 (2016) no. 7. http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a1/