Preimages under the Stack-Sorting Algorithm
Colin Defant

TL;DR
This paper develops a method to determine preimages under the stack-sorting map, leading to improved upper bounds on the growth rates of t-stack sortable permutations for t=3 and 4.
Contribution
It introduces a recursive approach to bound the number of preimages, enhancing existing bounds for the asymptotic growth of t-stack sortable permutations.
Findings
Significantly improved upper bounds for t=3 and t=4.
Derived recursive bounds for permutation counts.
Enhanced understanding of permutation preimages under stack-sorting.
Abstract
We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers and of -stack sortable permutations of length and -stack sortable permutations of length with exactly descents. From these bounds, we are able to significantly improve the best known upper bounds for when and .
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Biochemical and Structural Characterization · Algorithms and Data Compression
