Geodesic
Using Lovász local lemma in the space of random injections
The electronic journal of combinatorics, Tome 14 (2007)
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The Lovász Local Lemma is known to have an extension for cases where independence is missing but negative dependencies are under control. We show that this is often the case for random injections, and we provide easy-to-check conditions for the non-trivial task of verifying a negative dependency graph for random injections. As an application, we prove existence results for hypergraph packing and Turán type extremal problems. A more surprising application is that tight asymptotic lower bounds can be obtained for asymptotic enumeration problems using the Lovász Local Lemma.
DOI : 10.37236/981
Classification : 05D40, 05A16, 60C05, 05C35, 05C70, 05C80
Mots-clés : dependency graph, negative dependency graph, Lovasz local lemma, random injections, permutation enumeration, hzpergraph packing, Turan-type extremal problems 
@article{10_37236_981,
     author = {Linyuan Lu and L\'aszl\'o Sz\'ekely},
     title = {Using {Lov\'asz} local lemma in the space of random injections},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/981},
     zbl = {1183.05088},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/981/}
}
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%A László Székely
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Linyuan Lu; László Székely. Using Lovász local lemma in the space of random injections. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/981

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