On the geometry of stack-sorting simplices

2025/07/31 by Ake, Cameron, Lewis, Spencer F., Louie, Amanda +1
#05A15 #52B05 #52B20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.00219

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.

Citations

• Catalan Intervals and Uniquely Sorted Permutations
• A Diagonal on the Associahedra

Related

• Stack-sorting simplices: geometry and lattice-point enumeration
• Enumeration of lattice polytopes by their volume
• The lattice points of a stacky polytope
• A characterization of simplicial polytopes with g₂=1
• Lectures on 0/1-polytopes