Counting maximal antichains and independent sets

Details Counting maximal antichains and independent sets Counting maximal antichains and independent sets

2012-02-20

arxiv.org/abs/1202.4427v1

Mathematics

Combinatorics

12 pages

Scientific paper

Answering several questions of Duffus, Frankl and R\"odl, we give asymptotics for the logarithms of (i) the number of maximal antichains in the n-dimensional Boolean algebra and (ii) the numbers of maximal independent sets in the covering graph of the n-dimensional hypercube and certain natural subgraphs thereof. The results in (ii) are implied by more general upper bounds on the numbers of maximal independent sets in regular and biregular graphs. We also mention some stronger possibilities involving actual rather than logarithmic asymptotics.

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