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Weakly union-free maximum packings

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Abstract

Frankl and Füredi [11] established that the largest number of 3-subsets of ann-set, for which no four distinct setsA,B,D satisfyAB=CD, is at most\(\left\lfloor {\frac{{n(n - 1)}}{3}} \right\rfloor\). Chee, Colbourn, and Ling [6] established that this upper bound is met with few exceptions whenn≡0, 1 (mod 3). In this paper, it is established that the upper bound is also met with few exceptions whenn≡2 (mod 3).

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The research was supported in part by the US Army Research Office under Grant DAAG55-98-1-0272.

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Colbourn, C.J. Weakly union-free maximum packings. Annals of Combinatorics 3, 43–52 (1999). https://doi.org/10.1007/BF01609874

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