An enumeration of spherical latin bitrades

TL;DR

This paper presents computational enumeration results for spherical Latin bitrades, which are pairs of partial Latin squares with specific disjointness and embedding properties, up to size 24.

Contribution

It provides the first extensive enumeration of spherical Latin bitrades, linking combinatorial structures to topological embeddings and computational methods.

Findings

Enumerated spherical Latin bitrades up to size 24

Established counts and classifications for genus 0 cases

Connected combinatorial properties with topological embeddings

Abstract

A latin bitrade (T1, T2) is a pair of partial latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. A genus may be associated to a latin bitrade by constructing an embedding of the underlying graph in an oriented surface. We report computational enumeration results on the number of spherical (genus 0) latin bitrades up to size 24.