Rises in forests of binary shrubs

TL;DR

This paper investigates the statistical patterns called rise statistics in permutations linked to forests of binary shrubs, deriving generating functions to understand their distribution.

Contribution

It introduces five types of rise statistics for permutations associated with binary shrub forests and computes their generating functions.

Findings

Derived generating functions for five rise statistics

Enhanced understanding of permutation patterns in binary shrub forests

Provided analytical tools for future combinatorial studies

Abstract

The study of patterns in permutations associated with forests of binary shrubs was initiated by D. Bevan et al.. In this paper, we study five different types of rise statistics that can be associated with such permutations and find the generating functions for the distribution of such rise statistics.