Patrick Eads

Date of Award


Document Type


Degree Name

Master of Science (MS)


Mathematical Sciences

Committee Chair

Guo-Hui Zhang

Committee Member

Daniel Bossaller

Committee Member

Shanbing Ai


Magic squares, Moufang loops, Combinatorial analysis


A Latin square in an n x n array of symbols in which each row and each column is a permutation of the n symbols. A selection of n cells from this array that lie on different rows and different columns and contain all n symbols is a transversal of the Latin square. Two longstanding conjectures concern the existence of transversals, Ryser’s conjecture and Brualdi’s conjecture. This thesis examines some of the results that have been achieved in investigating these conjectures, particularly in the cases of Latin squares generated from the Cayley tables of non-associative algebraic structures. A new method for constructing these transversals is demonstrated and the implications of this approach for future work is discussed.



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