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On independent sets. (English) Zbl 1112.05014
Summary: In a general set-theoretic context, an independent set is defined as a set which avoids certain specified structures called blocks. A formula is given for the number of independent sets of cardinality \(k\) in terms of the numbers of configurations (i.e., non-empty collections) of blocks.
MSC:
05B05 Combinatorial aspects of block designs
05A15 Exact enumeration problems, generating functions
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References:
[1] FORBES A. D.-GRANNELL M. J.-GRIGGS T. S.: Independent sets in Steiner triple systems. Ars Combin. 72 (2004), 161-169. · Zbl 1069.05009
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