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A000479 Number of 1-factorizations of K_{n,n}. 10

%I #44 Jul 10 2023 08:19:54

%S 1,1,1,2,24,1344,1128960,12198297600,2697818265354240,

%T 15224734061278915461120,2750892211809148994633229926400,

%U 19464657391668924966616671344752852992000

%N Number of 1-factorizations of K_{n,n}.

%C Also, number of Latin squares of order n with first row 1,2,...,n.

%C Also number of fixed diagonal Latin squares of order n. - _Eric W. Weisstein_, Dec 18 2005

%C Also maximum number of Latin squares of order n such that no two of them have all the same rows (respectively, columns). - _Rick L. Shepherd_, Mar 01 2008

%D CRC Handbook of Combinatorial Designs, 1996, p. 660.

%D Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.

%H B. D. McKay, A. Meynert and W. Myrvold, <a href="http://users.cecs.anu.edu.au/~bdm/papers/ls_final.pdf">Small Latin Squares, Quasigroups and Loops</a>, J. Combin. Designs 15 (2007), no. 2, 98-119.

%H B. D. McKay and I. M. Wanless, <a href="http://dx.doi.org/10.1007/s00026-005-0261-7">On the number of Latin squares</a>, Ann. Combinat. 9 (2005) 335-344.

%H Artur Schaefer, <a href="http://arxiv.org/abs/1602.02186">Endomorphisms of The Hamming Graph and Related Graphs</a>, arXiv preprint arXiv:1602.02186 [math.CO], 2016.

%H D. S. Stones, <a href="https://doi.org/10.37236/487">The many formulas for the number of Latin rectangles</a>, Electron. J. Combin 17 (2010), A1.

%H D. S. Stones and I. M. Wanless, <a href="http://dx.doi.org/10.1016/j.jcta.2009.03.019">Divisors of the number of Latin rectangles</a>, J. Combin. Theory Ser. A 117 (2010), 204-215.

%H E. I. Vatutin, V. S. Titov, O. S. Zaikin, S. E. Kochemazov, S. U. Valyaev, A. D. Zhuravlev, M. O. Manzuk, <a href="http://evatutin.narod.ru/evatutin_co_ls_dls_9.pdf">Using grid systems for enumerating combinatorial objects with example of diagonal Latin squares</a>, Information technologies and mathematical modeling of systems (2016), pp. 154-157. (in Russian)

%H Vatutin E.I., Zaikin O.S., Zhuravlev A.D., Manzyuk M.O., Kochemazov S.E., Titov V.S., <a href="http://ceur-ws.org/Vol-1787/486-490-paper-84.pdf">Using grid systems for enumerating combinatorial objects on example of diagonal Latin squares</a>. CEUR Workshop proceedings. Selected Papers of the 7th International Conference Distributed Computing and Grid-technologies in Science and Education. 2017. Vol. 1787. pp. 486-490. urn:nbn:de:0074-1787-5.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LatinSquare.html">Latin Square</a>

%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>

%F a(n) = A000315(n)*(n-1)! = A002860(n)/n!.

%Y Cf. A000315, A000528, A002860.

%Y See A040082 and A264603 for other versions.

%K nonn,hard,nice

%O 0,4

%A _N. J. A. Sloane_

%E a(11) (from the McKay-Wanless article) from _Richard Bean_, Feb 17 2004

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)