General results on the enumeration of strings in Dyck paths
The electronic journal of combinatorics, Tome 18 (2011) no. 1
Let $\tau$ be a fixed lattice path (called in this context string) on the integer plane, consisting of two kinds of steps. The Dyck path statistic "number of occurrences of $\tau$" has been studied by many authors, for particular strings only. In this paper, arbitrary strings are considered. The associated generating function is evaluated when $\tau$ is a Dyck prefix (or a Dyck suffix). Furthermore, the case when $\tau$ is neither a Dyck prefix nor a Dyck suffix is considered, giving some partial results. Finally, the statistic "number of occurrences of $\tau$ at height at least $j$" is considered, evaluating the corresponding generating function when $\tau$ is either a Dyck prefix or a Dyck suffix.
@article{10_37236_561,
author = {K. Manes and A. Sapounakis and I. Tasoulas and P. Tsikouras},
title = {General results on the enumeration of strings in {Dyck} paths},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/561},
zbl = {1217.05028},
url = {http://geodesic.mathdoc.fr/articles/10.37236/561/}
}
TY - JOUR AU - K. Manes AU - A. Sapounakis AU - I. Tasoulas AU - P. Tsikouras TI - General results on the enumeration of strings in Dyck paths JO - The electronic journal of combinatorics PY - 2011 VL - 18 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.37236/561/ DO - 10.37236/561 ID - 10_37236_561 ER -
K. Manes; A. Sapounakis; I. Tasoulas; P. Tsikouras. General results on the enumeration of strings in Dyck paths. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/561
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