Packings of pairs with a minimum known number
of quadruples

Abstract: 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.

Keywords: packing of pairs with quadruples, system of quadruples, configuration, packing of $K_4$'s into $K_n$.

Classification (MSC91): 05B40, 05B05

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