An enumeration of spherical latin bitrades
Ales Drapal, Carlo Hamalainen, Dan Rosendorf

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.
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Taxonomy
Topicsgraph theory and CDMA systems · semigroups and automata theory · Digital Image Processing Techniques
