The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
OFFSET
1,4
COMMENTS
Number of essentially different ways of scheduling a tournament of 2n teams.
REFERENCES
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.
LINKS
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.
D. V. Zinoviev, On the number of 1-factorizations of a complete graph [in Russian], Problemy Peredachi Informatsii, 50 (No. 4), 2014, 71-78.
FORMULA
a(n) ~ exp(2n^2 log(2n)) as n -> infinity (see CRC Handbook, p. 655, Theorem 4.20).
CROSSREFS
For odd n this sequence equals A350017. Cf. A000438.
Sequence in context: A289894 A058807 A350017 * A291593 A029591 A151578
KEYWORD
nonn,hard,more,nice
AUTHOR
EXTENSIONS
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
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 09:43 EDT 2024. Contains 373383 sequences. (Running on oeis4.)