Displaying similar documents to “Embedding 3 -homogeneous latin trades into abelian 2 -groups”

A uniqueness result for 3 -homogeneous latin trades

Nicholas J. Cavenagh (2006)

Commentationes Mathematicae Universitatis Carolinae

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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...

Overlapping latin subsquares and full products

Joshua M. Browning, Petr Vojtěchovský, Ian M. Wanless (2010)

Commentationes Mathematicae Universitatis Carolinae

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We derive necessary and sufficient conditions for there to exist a latin square of order n containing two subsquares of order a and b that intersect in a subsquare of order c . We also solve the case of two disjoint subsquares. We use these results to show that: (a) A latin square of order n cannot have more than n m n h / m h subsquares of order m , where h = ⌈ ( m + 1 ) / 2 ⌉ . Indeed, the number of subsquares of order m is bounded by a polynomial of degree at most 2 m + 2 in n . (b) For all n ≥ 5 there exists a loop of order...