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ON THE NUMBER OF LATIN RECTANGLES

Published online by Cambridge University Press:  22 June 2010

DOUGLAS S. STONES*
Affiliation:
School of Mathematical Sciences, Monash University, Vic 3800, Australia (email: the_empty_element@yahoo.com)
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Abstract

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Type
Abstracts of Australasian PhD Theses
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Alon, N. and Tarsi, M., ‘Colorings and orientations of graphs’, Combinatorica 12(2) (1992), 125134.CrossRefGoogle Scholar
[2]Bryant, D., Buchanan, M. and Wanless, I. M., ‘The spectrum for quasigroups with cyclic automorphisms and additional symmetries’, Discrete Math. 304(4) (2009), 821833.CrossRefGoogle Scholar
[3]Carlitz, L., ‘Congruences connected with three-line Latin rectangles’, Proc. Amer. Math. Soc. 4(1) (1953), 911.CrossRefGoogle Scholar
[4]Clark, D. and Lewis, J. T., ‘Transversals of cyclic Latin squares’, Congr. Numer. 128 (1997), 113120.Google Scholar
[5]Denés, J. and Keedwell, A. D., Latin Squares and their Applications (Academic Press, New York, 1974).Google Scholar
[6]Doyle, P. G., ‘The number of Latin rectangles’, arXiv:math/0703896v1 [math.CO], 15 pp.Google Scholar
[7]Drisko, A. A., ‘On the number of even and odd Latin squares of order p+1’, Adv. Math. 128(1) (1997), 2035.CrossRefGoogle Scholar
[8]Evans, A. B., Orthomorphism Graphs of Groups (Springer, Berlin, 1992).CrossRefGoogle Scholar
[9]McKay, B. D., Meynert, A. and Myrvold, W., ‘Small Latin squares, quasigroups and loops’, J. Combin. Des. 15 (2007), 98119.CrossRefGoogle Scholar
[10]McKay, B. D. and Wanless, I. M., ‘On the number of Latin squares’, Ann. Comb. 9 (2005), 335344.CrossRefGoogle Scholar
[11]Riordan, J., ‘A recurrence relation for three-line Latin rectangles’, Amer. Math. Monthly 59(3) (1952), 159162.CrossRefGoogle Scholar
[12]Stones, D. S., ‘The many formulae for the number of Latin rectangles’, Electron. J. Combin. 17 (2010), A1.CrossRefGoogle Scholar
[13]Stones, D. S., ‘The parity of the number of quasigroups’, submitted.Google Scholar
[14]Stones, D. S., ‘On the number of Latin rectangles’. PhD Thesis, Monash University, 2010.CrossRefGoogle Scholar
[15]Stones, D. S., Vojtěchovský, P. and Wanless, I. M., ‘Autotopisms and automorphisms of Latin squares’, in preparation (working title).Google Scholar
[16]Stones, D. S. and Wanless, I. M., ‘Compound orthomorphisms of the cyclic group’, Finite Fields Appl. 16 (2010), 277289.CrossRefGoogle Scholar
[17]Stones, D. S. and Wanless, I. M., ‘A congruence connecting Latin rectangles and partial orthomorphisms’, submitted.Google Scholar
[18]Stones, D. S. and Wanless, I. M., ‘How not to prove the Alon–Tarsi conjecture’, submitted.Google Scholar
[19]Stones, D. S. and Wanless, I. M., ‘Divisors of the number of Latin rectangles’, J. Combin. Theory Ser. A 117(2) (2010), 204215.CrossRefGoogle Scholar
[20]Wanless, I. M., ‘Diagonally cyclic Latin squares’, European J. Combin. 25 (2004), 393413.CrossRefGoogle Scholar