Abstract:
Let a and b be positive integers, an (a; b)sudoku-pair Latin square is a Latin square of
order ab with an additional property that there is no repetition of symbols in any canonical
a b and b a tiling region. It is currently unknown whether a sudoku-pair Latin square
exists for every pair of integers a and b. In this thesis I provide two group-theoretic construction
methods to help us get closer to solving this open problem. This also allows us to
create many concrete examples.
One construction will produce sudoku-pair Latin squares of order ab when ajb. The
second construction will produce, under a few constraints, sudoku-pair Latin squares when
a and b are relatively prime. In order to accomplish this latter task, a new idea called
the gnomon condition is presented, which is a tool that gives the ability to confirm a valid
sudoku-pair Latin square without needing to check the entire grid.
