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- W2516660082 abstract "In 1975, Lovász conjectured that any maximal intersecting family of $k$-sets has at most $lfloor(e-1)k!rfloor$ blocks, where $e$ is the base of the natural logarithm. This conjecture was disproved in 1996 by Frankl and his co-authors. In this short note, we reprove the result of Frankl et al. using a vastly simplified construction of maximal intersecting families with many blocks. This construction yields a maximal intersecting family $mathbb{G}_{k}$ of $k-$sets whose number of blocks is asymptotic to $e^{2}(frac{k}{2})^{k-1}$ as $krightarrowinfty$." @default.
- W2516660082 created "2016-09-16" @default.
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- W2516660082 date "2016-08-19" @default.
- W2516660082 modified "2023-09-26" @default.
- W2516660082 title "A New Construction of Non-Extendable Intersecting Families of Sets" @default.
- W2516660082 doi "https://doi.org/10.37236/5976" @default.
- W2516660082 hasPublicationYear "2016" @default.
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