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Dyck Paths with Peak- and Valley-Avoiding Sets

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In this paper, we focus on Dyck paths with peaks and valleys, avoiding 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 and valley heights to avoid congruence classes modulo k. We study the shift equivalence on sequences, which in turn induces an equivalence relation on avoiding sets.
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Document Type: Research Article

Affiliations: National Hsinchu University of Education, Taiwan Academia Sinica, Taiwan

Publication date: October 1, 2008

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