On the geometry of stack-sorting simplices

Authors

  • Cameron Ake Harvey Mudd College
  • Spencer F. Lewis Harvey Mudd College
  • Amanda Louie Harvey Mudd College
  • Andrés R. Vindas Meléndez Harvey Mudd College

DOI:

https://doi.org/10.63151/amjc.v4i.35

Keywords:

stack-sorting algorithm, simplices, polytope, permutation, relative volume

Abstract

We show that all stack-sorting polytopes are simplices. Furthermore, we show that the stack-sorting polytopes generated from permutations of the form \(Ln1\) have relative volume 1. We establish an upper bound for the number of lattice points in a stack-sorting polytope. In particular, stack-sorting polytopes generated from permutations of the form \(2Ln1\) have no interior points.

 

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Published

2025-08-21

Issue

Vol. 4 (2025)

Section

Articles

License

Copyright (c) 2025 Cameron Ake, Spencer F. Lewis, Amanda Louie, Andrés R. Vindas Meléndez

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.