We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if is even.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1440, author = {Artur Szyma\'nski and A. Pawe\l\ Wojda}, title = {A note on k-uniform self-complementary hypergraphs of given order}, journal = {Discussiones Mathematicae Graph Theory}, volume = {29}, year = {2009}, pages = {199-202}, zbl = {1189.05119}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1440} }
Artur Szymański; A. Paweł Wojda. A note on k-uniform self-complementary hypergraphs of given order. Discussiones Mathematicae Graph Theory, Tome 29 (2009) pp. 199-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1440/
[000] [1] J.W.L. Glaisher, On the residue of a binomial coefficient with respect to a prime modulus, Quarterly Journal of Mathematics 30 (1899) 150-156. | Zbl 29.0152.03
[001] [2] S.H. Kimball, T.R. Hatcher, J.A. Riley and L. Moser, Solution to problem E1288: Odd binomial coefficients, Amer. Math. Monthly 65 (1958) 368-369, doi: 10.2307/2308812.
[002] [3] W. Kocay, Reconstructing graphs as subsumed graphs of hypergraphs, and some self-complementary triple systems, Graphs Combin. 8 (1992) 259-276, doi: 10.1007/BF02349963. | Zbl 0759.05064
[003] [4] G. Ringel, Selbstkomplementäre Graphen, Arch. Math. 14 (1963) 354-358, doi: 10.1007/BF01234967.
[004] [5] H. Sachs, Über selbstkomplementäre Graphen, Publ. Math. Debrecen 9 (1962) 270-288. | Zbl 0119.18904
[005] [6] A. Szymański, A note on self-complementary 4-uniform hypergraphs, Opuscula Math. 25/2 (2005) 319-323. | Zbl 1122.05067
[006] [7] A.P. Wojda, Self-complementary hypergraphs, Discuss. Math. Graph Theory 26 (2006) 217-224, doi: 10.7151/dmgt.1314. | Zbl 1142.05058