English

On the geometry of stack-sorting simplices

Combinatorics 2025-08-04 v1

Abstract

We show that all stack-sorting polytopes are simplices. Furthermore, we show that the stack-sorting polytopes generated from Ln1Ln1 permutations 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 2Ln12Ln1 permutations have no interior points.

Keywords

Cite

@article{arxiv.2508.00219,
  title  = {On the geometry of stack-sorting simplices},
  author = {Cameron Ake and Spencer F. Lewis and Amanda Louie and Andrés R. Vindas-Meléndez},
  journal= {arXiv preprint arXiv:2508.00219},
  year   = {2025}
}

Comments

15 pages, 4 figures, comments welcomed!

R2 v1 2026-07-01T04:28:41.471Z