Combinatorial Designs and Availability
Résumé
We consider a variation of Design Theory, in which the elements of the base set may be “available” or not. The random variable of interest is the number of subsets in the design which contain some available element. We are particularly interested in the variance of this variable, and we look for arrangements which minimize this value. We provide the solution to some instances of this problem; we show in particular that Steiner systems optimize this function.
Domaines
Mathématique discrète [cs.DM]
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