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A transvection decomposition in GL(n,2)

Clorinda De Vivo, Claudia Metelli (2002)

Colloquium Mathematicae

An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.

A uniqueness result for 3 -homogeneous latin trades

Nicholas J. Cavenagh (2006)

Commentationes Mathematicae Universitatis Carolinae

A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A k -homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either 0 or k times. In this paper, we show that a construction given by Cavenagh, Donovan and Drápal for 3 -homogeneous latin trades in fact classifies every minimal 3 -homogeneous latin trade. We in turn classify all 3 -homogeneous latin trades. A corollary is that any 3 -homogeneous...

About a generalization of transversals

Martin Kochol (1994)

Mathematica Bohemica

The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.

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