### Abstract

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 language | English (US) |
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Title of host publication | Developments in Mathematics |

Publisher | Springer New York LLC |

Pages | 155-165 |

Number of pages | 11 |

DOIs | |

State | Published - Jan 1 2019 |

### Publication series

Name | Developments in Mathematics |
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Volume | 58 |

ISSN (Print) | 1389-2177 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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

## Cite this

*Developments in Mathematics*(pp. 155-165). (Developments in Mathematics; Vol. 58). Springer New York LLC. https://doi.org/10.1007/978-3-030-11102-1_8