The number of orientable small covers over cubes

TL;DR

This paper counts orientable small covers over n-dimensional cubes and provides estimates for the ratio of orientable to all small covers, advancing understanding of their classification.

Contribution

It introduces a method to count orientable small covers over cubes and estimates their proportion among all small covers, a novel contribution in the field.

Findings

Count of orientable small covers over cubes is established.

Estimates for the ratio O_n/R_n are provided.

Results enhance classification of small covers over cubes.

Abstract

We count orientable small covers over cubes. We also get estimates for $O_n/R_n$, where $O_n$ is the number of orientable small covers and $R_n$ is the number of all small covers over an $n$-cube up to the Davis-Januszkiewicz equivalence.