A description of the Zeta map on Dyck paths area sequences

TL;DR

This paper provides an accessible description of the Zeta map on Dyck paths using area sequences, facilitating easier implementation and understanding of its combinatorial properties.

Contribution

It offers a new, straightforward description of the Zeta map on Dyck paths via area sequences, enhancing computational and theoretical analysis.

Findings

The Zeta map transforms dinv and area statistics to area and bounce statistics.

The description using area sequences simplifies implementation.

The approach improves understanding of Dyck path combinatorics.

Abstract

We give a 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.