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arXiv · 2508.00219

On the geometry of stack-sorting simplices

Cameron Ake·Spencer F. Lewis·Amanda Louie·Andrés R. Vindas-Meléndez
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Abstract

We show that all stack-sorting polytopes are simplices. Furthermore, we show that the stack-sorting polytopes generated from $Ln1$ 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 $2Ln1$ permutations have no interior points.

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Cameron Ake, Spencer F. Lewis, Amanda Louie, Andrés R. Vindas-Meléndez. 2025-07-31. On the geometry of stack-sorting simplices. https://arxiv.org/abs/2508.00219

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