Counting strings in Dyck paths. (English) Zbl 1127.05005
Summary: This paper deals with the enumeration of Dyck paths according to the statistic “number of occurrences of \(\tau \),” for an arbitrary string \(\tau \). In this direction, the statistic “number of occurrences of \(\tau \) at height \(j\)” is considered. It is shown that the corresponding generating function can be evaluated with the aid of Chebyshev polynomials of the second kind. This is applied to every string of length 4. Further results are obtained for the statistic “number of occurrences of \(\tau \) at even (or odd) height.”
MSC:
| 05A15 | Exact enumeration problems, generating functions |
Software:
OEISReferences:
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