A036981 -id:A036981 - cp's OEIS frontend

CRC Handbook of Combinatorial Designs (see pages 655, 720-723).
N. T. Gridgeman, Latin Squares Under Restriction and a Jumboization, J. Rec. Math., 5 (1972), 198-202.
W. D. Wallis, 1-Factorizations of complete graphs, pp. 593-631 in Jeffrey H. Dinitz and D. R. Stinson, Contemporary Design Theory, Wiley, 1992.

Jeffrey H. Dinitz, David K. Garnick, and Brendan D. McKay, There are 526,915,620 nonisomorphic one-factorizations of K_{12}, J. Combin. Des. 2 (1994), no. 4, 273-285.
Alan Hartman, and Alexander Rosa, Cyclic one-factorization of the complete graph, European J. Combin. 6 (1985), no. 1, 45-48.
Dieter Jungnickel, and Vladimir D. Tonchev, Counting Steiner triple systems with classical parameters and prescribed rank, arXiv:1709.06044 [math.CO], 2017.
Petteri Kaski, and Patric R. J. Östergård, There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations of K14, Journal of Combinatorial Designs 17 (2009) 147-159.
Mario Krenn, Xuemei Gu, and Anton Zeilinger, Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings, arXiv:1705.06646 [quant-ph], 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."]
D. V. Zinoviev, On the number of 1-factorizations of a complete graph [in Russian], Problemy Peredachi Informatsii, 50 (No. 4), 2014, 71-78.
Index entries for sequences related to tournaments

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

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

A036980 Number of (2n) X (2n) symmetric matrices each of whose rows is a permutation of 1..(2n).

Original entry on oeis.org

1, 2, 96, 328320, 440952422400

Offset: 0

Joshua Zucker and Joe Keane

Cf. A035481, A036981.

a(n) = A035483(n) * (2n)!

A035482 Number of n X n symmetric matrices each of whose rows is a permutation of 1..n.

Original entry on oeis.org

1, 1, 2, 6, 96, 720, 328320, 31449600, 440952422400, 444733651353600, 471835793808949248000, 10070314878246926155776000, 1058410183156945383046388908032000, 614972203951464612786852376432607232000

Offset: 0

Joshua Zucker and Joe Keane

The even and odd subsequences are A036980, A036981.

			a(3) = 6 because the first row is arbitrary (say, 213) and the rest is then determined. By symmetry the second row has to be 132 or 123 but in order for the third row/column to work it has to be 132.

Cf. A000438, A035481, A000315, A002860, A003090, A040082.

a(n) = A035481(n) * n!. [From Max Alekseyev, Apr 23 2010]

a(10)-a(13) (using A035481) from Alois P. Heinz, May 05 2023

cp's OEIS Frontend

A064120 A036981(n)/n!^2.

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A065594 a(n) = A036981(n)/(2n)!.

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A289747 Erroneous version of A036981.

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A000438 Number of 1-factorizations of complete graph K_{2n}.

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A036980 Number of (2n) X (2n) symmetric matrices each of whose rows is a permutation of 1..(2n).

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A035482 Number of n X n symmetric matrices each of whose rows is a permutation of 1..n.

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