Dyck Paths with Peaks Avoiding or Restricted to a Given Set

@article{Eu2003DyckPW,
title={Dyck Paths with Peaks Avoiding or Restricted to a Given Set},
author={Sen-Peng Eu and Shu-Chung Liu and Yeong-Nan Yeh},
journal={Studies in Applied Mathematics},
year={2003},
volume={111}
}
• Published 1 November 2003
• Mathematics
• Studies in Applied Mathematics
In this paper we focus on Dyck paths with peaks avoiding or restricted to an arbitrary set of heights. The generating functions of such types of Dyck paths can be represented by continued fractions. We also discuss a special case that requires all peak heights to either lie on or avoid a congruence class (or classes) modulo k. The case when k= 2 is especially interesting. The two sequences for this case are proved, combinatorially as well as algebraically, to be the Motzkin numbers and the…
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