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A000474 Number of nonisomorphic 1-factorizations of complete graph K_{2n}. 4
1, 1, 1, 6, 396, 526915620, 1132835421602062347 (list; graph; refs; listen; history; text; internal format)



Number of essentially different ways of scheduling a tournament of 2n teams.


CRC Handbook of Combinatorial Designs (see pages 655, 720-723).

Jeffrey H. Dinitz, David K. Garnick, Brendan D. McKay, There are 526,915,620 nonisomorphic one-factorizations of K_{12}. J. Combin. Des. 2 (1994), no. 4, 273-285.

Petteri Kaski and Patric R. J. Östergård, There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations of K_{14}, Journal of Combinatorial Designs 17 (2009), pp. 147-159.

Charles C. Lindner, Eric Mendelsohn, and Alexander Rosa. "On the number of 1-factorizations of the complete graph." Journal of Combinatorial Theory, Series B 20.3 (1976): 265-282.

E. Seah and D. R. Stinson, On the enumeration of one-factorizations of complete graphs containing prescribed automorphism groups. Math. Comp. 50 (1988), 607-618.

W. D. Wallis, 1-Factorizations of complete graphs, pp. 593-631 in Jeffrey H. Dinitz and D. R. Stinson, Contemporary Design Theory, Wiley, 1992.

D. V. Zinoviev, On the number of 1-factorizations of a complete graph [in Russian], Problemy Peredachi Informatsii, 50 (No. 4), 2014, 71-78.


Table of n, a(n) for n=1..7.

Petteri Kaski and Patric R. J. Östergård, There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations of K_{14}, arXiv:0801.0202 [math.CO], 2007.

Joseph Malkevitch, Mathematics and Sports

Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, arXiv:2104.07902 [math.CO], 2021. Table 5 p. 15.

Index entries for sequences related to tournaments


a(n) ~ exp(2n^2 log(2n)) as n -> infinity (see CRC Handbook, p. 655, Theorem 4.20).


For odd n this sequence equals A350017. Cf. A000438.

Sequence in context: A289894 A058807 A350017 * A291593 A029591 A151578

Adjacent sequences: A000471 A000472 A000473 * A000475 A000476 A000477




N. J. A. Sloane


a(7) communicated by Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Aug 02 2008

Comment, link, and update by Charles R Greathouse IV, May 11 2010



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