Generalizations of two-stack-sortable permutations

TL;DR

This paper extends the concept of two-stack-sortable permutations to r-permutations, deriving explicit formulas and solving functional equations to count these permutations based on descents.

Contribution

It introduces a novel approach to analyze two-stack-sortable r-permutations and provides explicit enumeration formulas using functional equations.

Findings

Derived the functional equation for generating functions of two-stack-sortable r-permutations.

Solved the functional equation to obtain explicit formulas for counting permutations.

Extended the analysis of stack sorting to r-permutations with new enumeration results.

Abstract

In this thesis, we apply the stack sorting operator to $r$-permutations and construct the functional equation for the generating function of two-stack-sortable $k$-tuple $r$-permutations counted by descents by using a factorization similar to Zeilberger's. We solve the functional equation and give explicit formulas for the number of two-stack-sortable $r$-permutations.