Ehrhart polynomials of convex polytopes with small volumes

TL;DR

This paper classifies all possible delta-vectors of d-dimensional integral convex polytopes with volumes up to 3/(d!), providing a comprehensive understanding of their combinatorial structures.

Contribution

It offers a complete classification of delta-vectors for small-volume convex polytopes, a previously unresolved problem in polytope theory.

Findings

Complete classification of delta-vectors for polytopes with volume ≤ 3/(d!)

Identification of possible delta-vectors in low-volume cases

Insights into the structure of small-volume convex polytopes

Abstract

We classify all the possible $delta$-vectors of d-dimensional integral convex polytopes whose volumes are less than or equal to 3/(d!).