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Keywords:
configuration; packing of pairs; quadruples; packing of pairs with quadruples; system of quadruples; packing of $K_4$'s into $K_n$
configuration; packing of pairs; quadruples; packing of pairs with quadruples; system of quadruples; packing of $K_4$'s into $K_n$
Summary:
Let $E$ be an $n$-set. The problem of packing of pairs on $E$ with a minimum number of quadruples on $E$ is settled for $n<15$ and also for $n=36t+i$, $i=3$, $6$, $9$, $12$, where $t$ is any positive integer. In the other cases of $n$ methods have been presented for constructing the packings having a minimum known number of quadruples.
References:
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[2] H. Hanani: The existence and construction of balanced incomplete block design. Ann. Math. Statist. 32 (1961), 361-386. DOI 10.1214/aoms/1177705047 | MR 0166888
[3] J. Novák: Edge-bases of complete uniform hypergraphs. Mat. čas. 24 (1974), 43-57. MR 0357242
[4] C. Colbourn A. Rosa Š. Znám: The spectrum of maximal partial Steiner triple systems. Math. Reports Mc. Master University. 1991.
[5] P. Turán: On the theory of graphs. Colloq. Math. 3 (1955), 19-30. MR 0062416
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