On face numbers of neighborly cubical polytopes

TL;DR

This paper derives an explicit formula for the face numbers of neighborly cubical polytopes, showing they form a unimodal sequence, thus advancing understanding of their combinatorial structure.

Contribution

It provides the first explicit formula for face numbers of neighborly cubical polytopes using cubical h-vectors, revealing their unimodal nature.

Findings

Face numbers are explicitly calculated.

Face number sequence is unimodal.

Utilizes cubical h-vectors for derivation.

Abstract

Neighborly cubical polytopes are known as the cubical analogues of the cyclic polytopes. Using the short cubical $h$-vectors of cubical polytopes (introduced by Adin), we derive an explicit formula for the face numbers of the neighborly cubical polytopes. These face numbers form a unimodal sequence.