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http://dx.doi.org/10.5831/HMJ.2021.43.4.641

ENUMERATION OF FUSS-CATALAN PATHS BY TYPE AND BLOCKS

An, Suhyung (Department of Mathematics, Yonsei University)
Jung, JiYoon (Department of Mathematics, Marshall University)
Kim, Sangwook (Department of Mathematics, Chonnam National University)

Publication Information

Honam Mathematical Journal / v.43, no.4, 2021 , pp. 641-653 More about this Journal

Abstract

Armstrong enumerated the number of Fuss-Catalan paths with a given type and Rhoades provided the number of Dyck paths with a given type and a given number of blocks. In this paper we generalize those results to enumerate the number of Fuss-Catalan paths with a fixed type and a fixed number of blocks. We provide two proofs of this result. The first one uses the Chung-Feller theorem and a certain polynomial, while the second one is bijective. Also, we give a conjecture generalizing this result to the family of small Fuss-Schröder paths.

Keywords

Dyck paths; Fuss-Catalan paths; type; block;

Citations & Related Records

Reference

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