### (Department of Mathematics, University of Manitoba)

*Orienting wide partitions*

Date | Friday, March 16, 2018 |
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Latin squares are square arrays filled with symbols so that every symbol appears exactly once in each row and column. For example, Cayley tables and sudoku solutions are Latin squares. While it is simple to construct a Latin square with n symbols on a square array of size n, construction of Latin squares can become difficult when further constraints are imposed. Dinitz’s conjecture, which was confirmed by Galvin, relates to the existence of Latin squares when different cells have different sets of available symbols, Rota’s basis conjecture pertains to the problem when the symbols are vectors and rows/columns must be linearly independent, and the wide partition conjecture addresses the problem for shapes other than square arrays. I will discuss these problems and conjectures and my recent results on the wide partition conjecture. Based on joint work with Ping Kittipassorn.