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Cybernetics and Systems Analysis

, Volume 45, Issue 1, pp 69–75 | Cite as

Estimating the number of latin rectangles by the fast simulation method

  • N. Yu. Kuznetsov
Systems Analysis

A fast simulation method is proposed to estimate the number of Latin rectangles and squares. Numerous examples demonstrate the high accuracy of the method. The number of Latin squares of order n = 20 is estimated with a relative error of 5% and a confidence level of 0.99. Statistical lower bounds for the maximum number of transversals over all Latin squares of order n = 20 are obtained.

Keywords

Latin rectangle Latin square transversal fast simulation method unbiased estimate sample variance relative error 

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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