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 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 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!