Almost all sets of d+2 points on the (d-1)-sphere are not subtransitive

TL;DR

This paper demonstrates that nearly all configurations of d+2 points on a (d-1)-sphere cannot be embedded into a transitive set in any Euclidean space, extending previous arguments to a broader class of point sets.

Contribution

It generalizes an existing argument to show that almost all sets of d+2 points on the (d-1)-sphere are not subtransitive in any Euclidean space.

Findings

Most d+2 point sets on the (d-1)-sphere are not subtransitive.

The result extends previous work to a more general setting.

Almost all such point sets lack a transitive embedding.

Abstract

We generalise an argument of Leader, Russell, and Walters to show that almost all sets of d + 2 points on the (d - 1)-sphere S^{d-1} are not contained in a transitive set in some R^n.