Currently displaying 1 – 5 of 5

Showing per page

Order by Relevance | Title | Year of publication

Overlapping latin subsquares and full products

Joshua M. BrowningPetr VojtěchovskýIan M. Wanless — 2010

Commentationes Mathematicae Universitatis Carolinae

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 n in which every...

Page 1

Download Results (CSV)