Category Extremal Set Theory
Zarankiewicz’s Problem
Zarankiewicz’s problem plays an important role in extremal combinatorics. Let’s first learn few things about Kazimierz Zarankiewicz from Wikipedia. Unfortunately, his life had a lot of suffering. He had to live the nightmare of concentration camps during World War II and he was a revolutionary. He was not a guerrilla but continued to teach despite the Nazi […]
Ahlswede-Zhang identity
This post is about Sperner systems and about turning the famous LYM inequality into an identity. Typically, people refer to this inequality as the LYM inequality (Lubell-Yamamoto-Meshalkin) but it is worth pointing out that the inequality follows as a corollary from the more general Bollobás inequality. While thinking of this inequality I asked myself about the cases that […]
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