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{\bf Linyuan Lu and L\'aszl\'o Sz\'ekely }
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{\bf Using Lov\'asz Local Lemma in the Space of Random Injections}
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The Lov\'asz 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
Tur\'an type extremal problems. A more surprising application is that
tight asymptotic lower bounds can be obtained for asymptotic
enumeration problems using the Lov\'asz Local Lemma.



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