@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.}",

year = "2019",

month = jan,

day = "1",

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",

}