ON THE NUMBER AND EQUIVALENT LATIN SQUARES | ||
Journal of University of Anbar for Pure Science | ||
Article 16, Volume 1, Issue 1, April 2007, Pages 71-75 PDF (279.09 K) | ||
Document Type: Research Paper | ||
DOI: 10.37652/juaps.2007.15428 | ||
Author | ||
MAKARIM A. AL-TURKY* | ||
Computer College - Univesity of Al-Anbar | ||
Abstract | ||
we determine the number of Latin rectangles with 11 columns and each possible number of rows, In clouding the Latin squares of order11. Also answer some questions of Alter by showing that the number of reduced Latin squares of order n is divisible by Fi where f is a particular integer close to . | ||
Keywords | ||
Number; EQUIVALENT LATIN SQUARES | ||
References | ||
[1]. R. Alter, How many Latin squares are there? Amer. Math. Monthly, 82(1975) 632-634.
[2]. C. J. Colbourn and J. Dinitz (editors), CRC Handbook of combinatorial Design, CRC Press, Boca Raton, 1996.
[3]. G. L. Mullen, How many i-j reduced Latin squares are there? Amer.Math. Monthly,85 (1978) 751-752.
[4]. B. D. McKay and E.Rogoyski, Latin squares of order 10, Electronic J. combina-torics, 2 (1995)# N3 (4eP).
[5]. Charles F. Laywin and Gary L. Mullen, “ABrief Introdaction to Latin squares” in Discrete Mathematics uing Latin squares, 4-5 (New York: Johnwiley & Sons, Inc, 1998).
[6]. B. D. McKay, A. Meynert and W. Myrvold, small Latin squares. quasi groups and Loops, Submitted.
[7]. S. E. Bammel and J. Rothstein, the number of 9x9 Latin squares, Discrete Math., 11 (1975)93-95.
[8] Brendan D. McKay and I an M. wanless.” on the number of Latin squares’ Australian National University.
[9]. G. Kolesova, C.W. H. Lam and Thiel, on the number of 8x8 Latin squares, J combinatorial theory , ser .A, 54 (1990)143-148.
[10]. Jia-yashao and wan-di wei, a formula for the number of Latin squares, Discrete Math. 110 (1992) 293-296.
[11]. B. D. McKay, nauty user’s guide (version 1-5) Technical report TR-CS-90-20, computer science Dept. Australian National university, 1990. | ||
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