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Returns and hills on generalized Dyck paths
J. Integer Seq., 2016Summary: In 2009, Shapiro posed the following question: ``What is the asymptotic proportion of Dyck paths having an even number of hills?'' (see [\textit{G.-S. Cheon} et al., Eur. J. Comb. 31, No. 1, 120--128 (2010; Zbl 1184.05006)]). In this paper, we answer Shapiro's question, as well as a generalization of the question to ternary paths. We find that
Naiomi T. Cameron, Jillian E. McLeod
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Enumerative Combinatorics of Intervals in the Dyck Pattern Poset
Order, 2021Luca Ferrari +2 more
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Asymptotic behavior and the moderate deviation principle for the maximum of a Dyck path
Statistics and Probability Letters, 2012Termeh Kousha
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Enumerations of peaks and valleys on non-decreasing Dyck paths
Discrete Mathematics, 2018Eva Czabarka +2 more
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Nonleft peaks in Dyck paths: A combinatorial approach
Discrete Mathematics, 2014I Tasoulas, A Sapounakis, P Tsikouras
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Combinatorics of the zeta map on rational Dyck paths
Journal of Combinatorial Theory - Series A, 2016Christopher R H Hanusa, Cesar Ceballos
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Uniform bounds for exponential moment of maximum of a Dyck path
Electronic Communications in Probability, 2009Jean-François Marckert
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Enumerating symmetric and asymmetric peaks in Dyck paths
Discrete Mathematics, 2020Rigoberto Florez, José L Ramirez
exaly
Counting strings at height j in Dyck paths
Journal of Statistical Planning and Inference, 2011I Tasoulas, A Sapounakis, P Tsikouras
exaly
Enumerating several aspects of non-decreasing Dyck paths
Discrete Mathematics, 2019Rigoberto Florez, José L Ramirez
exaly