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A000438 Number of 1-factorizations of complete graph K_{2n}. 9
1, 1, 6, 6240, 1225566720, 252282619805368320, 98758655816833727741338583040 (list; graph; refs; listen; history; text; internal format)



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

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

N. T. Gridgeman, Latin Squares Under Restriction and a Jumboization, J. Rec. Math., 5 (1972), 198-202.

Hartman, Alan and Rosa, Alexander, Cyclic one-factorization of the complete graph. European J. Combin. 6 (1985), no. 1, 45-48.

W. D. Wallis, 1-Factorizations of complete graphs, pp. 593-631 in J. 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.

Dieter Jungnickel, Vladimir D. Tonchev, Counting Steiner triple systems with classical parameters and prescribed rank, arXiv:1709.06044 [math.CO], 2017.

Mario Krenn, Xuemei Gu, Anton Zeilinger, Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings, arXiv:1705.06646 [quant-ph], 2017 and PRL 119 240403. [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


Cf. A000474, A003191, A035481, A035483. Equals A036981 / (2n+1)!.

Sequence in context: A202969 A003191 A298272 * A061109 A219014 A013784

Adjacent sequences:  A000435 A000436 A000437 * A000439 A000440 A000441




N. J. A. Sloane


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 Ostergard and Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 19 2007



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Last modified November 14 14:35 EST 2018. Contains 317208 sequences. (Running on oeis4.)