Counting strings in Dyck paths |
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Authors: | A Sapounakis P Tsikouras |
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Institution: | Department of Informatics, University of Piraeus, 18534 Piraeus, Greece |
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Abstract: | This paper deals with the enumeration of Dyck paths according to the statistic “number of occurrences of τ”, for an arbitrary string τ. In this direction, the statistic “number of occurrences of τ 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 τ at even (or odd) height”. |
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Keywords: | 05C05 05C07 05A15 |
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