Counting pop-stacked permutations in polynomial time

TL;DR

This paper presents a polynomial-time algorithm for counting pop-stacked permutations, computes extensive sequence data, and analyzes the generating function's properties and asymptotic behavior.

Contribution

It introduces a novel polynomial-time counting algorithm for pop-stacked permutations and extends the known sequence to 1000 terms.

Findings

First 1000 terms of the counting sequence computed

Negative results on the nature of the generating function

Predicted asymptotic behavior of the sequence

Abstract

Permutations in the image of the pop-stack operator are said to be pop-stacked. We give a polynomial-time algorithm to count pop-stacked permutations up to a fixed length and we use it to compute the first 1000 terms of the corresponding counting sequence. Only the first 16 terms had previously been computed. With the 1000 terms we prove some negative results concerning the nature of the generating function for pop-stacked permutations. We also predict the asymptotic behavior of the counting sequence using differential approximation.