Atomic Latin squares based on cyclotomic orthomorphisms.
On the Brualdi-Liu conjecture for the even permanent.
A generalization of transversals for Latin squares.
Acyclic digraphs and eigenvalues of -matrices.
Overlapping latin subsquares and full products
We derive necessary and sufficient conditions for there to exist a latin square of order containing two subsquares of order and that intersect in a subsquare of order . We also solve the case of two disjoint subsquares. We use these results to show that: (a) A latin square of order cannot have more than subsquares of order , where . Indeed, the number of subsquares of order is bounded by a polynomial of degree at most in . (b) For all there exists a loop of order in which every...
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