

A000438


Number of 1factorizations of complete graph K_{2n}.


9




OFFSET

1,3


REFERENCES

CRC Handbook of Combinatorial Designs (see pages 655, 720723).
N. T. Gridgeman, Latin Squares Under Restriction and a Jumboization, J. Rec. Math., 5 (1972), 198202.
W. D. Wallis, 1Factorizations of complete graphs, pp. 593631 in Jeffrey H. Dinitz and D. R. Stinson, Contemporary Design Theory, Wiley, 1992.
D. V. Zinoviev, On the number of 1factorizations of a complete graph [in Russian], Problemy Peredachi Informatsii, 50 (No. 4), 2014, 7178.


LINKS

Table of n, a(n) for n=1..7.
Jeffrey H. Dinitz, David K. Garnick, and Brendan D. McKay, There are 526,915,620 nonisomorphic onefactorizations of K_{12}, J. Combin. Des. 2 (1994), no. 4, 273285.
Alan Hartman, and Alexander Rosa, Cyclic onefactorization of the complete graph, European J. Combin. 6 (1985), no. 1, 4548.
Dieter Jungnickel, Vladimir D. Tonchev, Counting Steiner triple systems with classical parameters and prescribed rank, arXiv:1709.06044 [math.CO], 2017.
Petteri Kaski, Patric R. J. Östergård, There are 1,132,835,421,602,062,347 nonisomorphic onefactorizations of K14, Journal of Combinatorial Designs 17 (2009) 147159.
Mario Krenn, Xuemei Gu, Anton Zeilinger, Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings, arXiv:1705.06646 [quantph], 2017 and Phys. Rev. Lett. 119, 240403, 2017. [Mario Krenn said in an email, "We would not have discovered this connection between quantum mechanical experiments and graph theory, thus the physical interpretations and all the generalisations we are developing right now, without you and A000438."]
Index entries for sequences related to tournaments


CROSSREFS

Cf. A000474, A003191, A035481, A035483. Equals A036981 / (2n+1)!.
Sequence in context: A202969 A003191 A298272 * A061109 A321983 A219014
Adjacent sequences: A000435 A000436 A000437 * A000439 A000440 A000441


KEYWORD

nonn,hard,more,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

For K_16 the answer is approximately 1.48 * 10^44 and for K_18 1.52 * 10^63.  Dinitz et al.
a(7) found by Patric Östergård and Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 19 2007


STATUS

approved



