Euler Coefficients and Restricted Dyck Paths

Details Euler Coefficients and Restricted Dyck Paths Euler Coefficients and Restricted Dyck Paths

2007-05-21

arxiv.org/abs/0705.3065v1

Mathematics

Combinatorics

15 pages

Scientific paper

We consider the problem of enumerating Dyck paths staying weakly above the
x-axis with a limit to the number of consecutive up steps, or a limit to the
number of consecutive down steps. We use Finite Operator Calculus to obtain
formulas for the number of all such paths reaching a given point in the first
quadrant. All our results are based on the Eulerian coefficients.

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