A description of the Zeta map on Dyck paths area sequences

Viviane Pons (1, 2, 3, 4)

1 LISN - Laboratoire Interdisciplinaire des Sciences du Numérique
2 GALaC - Graphes, Algorithmes et Combinatoire - LISN
3 CRM - Centre de recherches mathématiques (IRL3457)
4 IRL CRM-CNRS - International Research Lab

We give a simple iterative description of the well known Zeta map on Dyck paths which sends the dinv,area statistics to the area,bounce statistics. Our description uses Dyck paths area sequences and can be implemented easily.

Mots clés: Zeta map; Dyck paths

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Viviane Pons. A description of the Zeta map on Dyck paths area sequences. 2023. ⟨hal-04024002⟩