Log-concavity of face vectors of cyclic and ordinary polytopes

TL;DR

This paper proves that the face vectors of ordinary polytopes, which generalize cyclic polytopes, are log-concave, revealing a key combinatorial property of these geometric structures.

Contribution

It establishes the log-concavity of face vectors for ordinary polytopes, extending known results from cyclic polytopes to a broader class.

Findings

Face vectors of ordinary polytopes are log-concave.

Generalization from cyclic to ordinary polytopes.

Supports combinatorial and geometric analysis of polytopes.

Abstract

Ordinary polytopes are known as a non-simplicial generalization of the cyclic polytopes. The face vectors of ordinary polytopes are shown to be log-concave.