On the symplectic size of convex polytopes

TL;DR

This paper introduces a combinatorial formula for the Ekeland-Hofer-Zehnder capacity of convex polytopes in n, enabling analysis of its subadditivity property.

Contribution

It provides the first combinatorial formula for the capacity of convex polytopes, advancing understanding of symplectic invariants in convex geometry.

Findings

Derived a combinatorial formula for the capacity

Established a subadditivity property of the capacity

Enhanced tools for symplectic capacity computation

Abstract

In this paper we introduce a combinatorial formula for the Ekeland-Hofer-Zehnder capacity of a convex polytope in $\mathbb{R}^{2n}$. One application of this formula is a certain subadditivity property of this capacity.