Andre' permutations, right-to-left and left-to-right minima

TL;DR

This paper investigates the distribution of right-to-left and left-to-right minima in Andre' permutations, providing generating functions, asymptotics, and leveraging their tree-structure to unify the analysis of both permutation kinds.

Contribution

It introduces a unified approach to analyze minima distributions in Andre' permutations using their tree-structure, with explicit generating functions and asymptotic results.

Findings

Distribution of minima is the same for both kinds of Andre' permutations.

Provides explicit generating functions for minima distributions.

Derives asymptotic behavior of minima counts.

Abstract

We provide enumerative results concerning right-to-left minima and left- to-right minima in Andre' permutations of the first and second kind. For both the two kinds, the distribution of right-to-left and left-to-right minima is the same. We provide generating functions and associated asymptotics results. Our approach is based on the tree-structure of Andre' permutations.