@inbook{b3c7e84eb6164cc2abb5194ce0a402c3,
title = "Enumeration of colored dyck paths via partial bell polynomials",
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.",
author = "Daniel Birmajer and Gil, {Juan B.} and McNamara, {Peter R.W.} and Weiner, {Michael D.}",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.",
year = "2019",
doi = "10.1007/978-3-030-11102-1_8",
language = "English (US)",
series = "Developments in Mathematics",
publisher = "Springer New York LLC",
pages = "155--165",
booktitle = "Developments in Mathematics",
}