Enumeration of colored dyck paths via partial bell polynomials

Daniel Birmajer, Juan B. Gil, Peter R.W. McNamara, Michael D. Weiner

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations


We consider a class of lattice paths with certain restrictions on their ascents and down-steps and use them as building blocks to construct various families of Dyck paths. We let every building block P j take on c j colors and count all of the resulting colored Dyck paths of a given semilength. Our approach is to prove a recurrence relation of convolution type, which yields a representation in terms of partial Bell polynomials that simplifies the handling of different colorings. This allows us to recover multiple known formulas for Dyck paths and related lattice paths in a unified manner.

Original languageEnglish (US)
Title of host publicationDevelopments in Mathematics
PublisherSpringer New York LLC
Number of pages11
StatePublished - 2019

Publication series

NameDevelopments in Mathematics
ISSN (Print)1389-2177

All Science Journal Classification (ASJC) codes

  • General Mathematics


Dive into the research topics of 'Enumeration of colored dyck paths via partial bell polynomials'. Together they form a unique fingerprint.

Cite this