

A090741


Maximum number of transversals in a Latin square of order n.


7




OFFSET

1,3


COMMENTS

a(10) >= 5504 from Parker.
a(n) >= the number of transversals in a cyclic Latin square of the same order which for odd n is given by A006717((n1)/2).  Eduard I. Vatutin, Nov 04 2020


REFERENCES

J. W. Brown, F. Cherry, L. Most, M. Most, E. T. Parker, W. D. Wallis, Completion of the spectrum of orthogonal diagonal Latin squares, Lecture notes in pure and applied mathematics. 1992. Vol. 139. pp. 4349.
E. T. Parker, Computer investigations of orthogonal Latin squares of order 10, Proc. Sympos. Appl. Math., volume 15 (1963), 7381.


LINKS

Eduard Vatutin, Alexey Belyshev, Natalia Nikitina, Maxim Manzuk, Alexander Albertian, Ilya Kurochkin, Alexander Kripachev, and Alexey Pykhtin, Diagonalization and Canonization of Latin Squares, Supercomputing, Russian Supercomputing Days (RuSCDays 2023) Rev. Selected Papers Part II, LCNS Vol. 14389, Springer, Cham, 4861.


FORMULA

a(n) is asymptotically in between 3.2^n and 0.62^n n!. [McKay, McLeod, Wanless], [Cavenagh, Wanless].  Ian Wanless, Jul 30 2010


EXAMPLE

a(1), a(3), a(5), a(7) are from the group tables for Z_1, Z_3, Z_5 and Z_7 (see sequence A006717); a(4) and a(8) are from Z_2 x Z_2 and the noncyclic groups of order 8 (see Bedford).
a(9) = 2241 from Z_3 x Z_3.


CROSSREFS



KEYWORD

hard,more,nonn


AUTHOR



EXTENSIONS



STATUS

approved



