Date of Award
2023
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
Committee Chair
Guo-Hui Zhang
Committee Member
Daniel Bossaller
Committee Member
Shanbing Ai
Subject(s)
Magic squares, Moufang loops, Combinatorial analysis
Abstract
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.
Recommended Citation
Eads, Patrick, "On the existence of transversals in Latin squares generated from algebraic structures" (2023). Theses. 620.
https://louis.uah.edu/uah-theses/620