Lovász Local Lemma

The Lovász Local Lemma is a principle in probability and combinatorics that helps prove the existence of certain desirable outcomes in situations where events are somewhat dependent on each other. It states that if events occur with low enough probabilities and are not too strongly dependent on each other, it's possible to ensure that not all of them happen at the same time. This is particularly useful in problems involving large sets of possibilities, allowing us to find at least one scenario where undesirable events don't all occur, thereby guaranteeing a positive outcome in complex situations.