Generating functions for the area below some lattice paths

Donatella Merlini (1)

1 DSI - Dipartimento di Sistemi e Informatica

We study some lattice paths related to the concept ofgenerating trees. When the matrix associated to this kind of trees is a Riordan array $D=(d(t),h(t))$, we are able to find the generating function for the total area below these paths expressed in terms of the functions $d(t)$ and $h(t)$.

Mots clés: Generating functions; Riordan arrays; lattice paths; generating trees; area; internal path length.

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Géométrie algorithmique [cs.CG]

Donatella Merlini. Generating functions for the area below some lattice paths. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.217-228, ⟨10.46298/dmtcs.3323⟩. ⟨hal-01183918⟩