On the upper embedding of Steiner triple systems and Latin squares

TL;DR

This paper proves that any prescribed orientation of triples in Steiner triple systems or Latin squares of odd order can be embedded in an orientable surface with triangular faces and one large face.

Contribution

It establishes the existence of embeddings with specific orientations for Steiner triple systems and Latin squares of odd order, including a large face.

Findings

Embeddings exist with prescribed orientations.

Triangular face embeddings with one large face are possible.

Applicable to Steiner triple systems and Latin squares of odd order.

Abstract

It is proved that for any prescribed orientation of the triples of either a Steiner triple system or a Latin square of odd order, there exists an embedding in an orientable surface with the triples forming triangular faces and one extra large face.