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University of Regina Department of Mathematics and Statistics

University of Regina
Department of Mathematics and Statistics
Speaker: Qing Xiang * (University of Delaware)
Title: Exterior Algebras and Two Conjectures about Finite Abelian Groups
(Joint work with Tao Feng and Zhi-Wei Sun)
Time & Place: Monday, April 06, 3:30 - 4:30 pm, CL 410
In 1999, Hunter Snevily made the following conjecture:
Conjecture. Let G be an abelian group of odd order and let A, B G
satisfy |A| = |B| = k. Then the elements of A and B may be ordered
A = {a1, a2, . . . , ak} and B = {b1, b2, . . . , bk} so that the sums a1 + b1,
a2 + b2, . . . , ak + bk are pairwise distinct.
The motivation for this question comes from the study of Latin squares.
A transversal of a Latin square is a collection of cells, no two of which are
in the same row or column, and we say that a transversal is Latin if no two
of its cells contain the same symbol. Latin transversals are nice structures
to find in Latin squares. The above conjecture can be rephrased in terms of
Latin transversals as follows: Every k k submatrix of the addition table
of an abelian group of odd order has a Latin transversal. There is a related


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics