Division sudokus: Invariants, enumeration and multiple partitions

TL;DR

This paper explores division sudokus, a special class of latin squares with six conjugates as sudoku squares, introducing invariants, enumeration methods, and constructions using algebraic structures.

Contribution

It introduces invariants for division sudokus, enumerates them up to equivalence, and constructs examples using nearfields and affine geometry.

Findings

Enumeration of division sudokus up to equivalence

Development of invariants for classification

Construction of rich examples using algebraic methods

Abstract

A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division sudokus with respect to multiple partitions at the same time. We use nearfields and affine geometry to construct division sudokus of prime power rank that are rich in sudoku partitions.