

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.


LINKS

Mario Krenn, Xuemei Gu, and 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."]


CROSSREFS



KEYWORD

nonn,hard,more,nice


AUTHOR



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



