Author Archives: randomprojection
Visualizing the Configuration model
A way to generate a random -regular graph is via the configuration model. Here is a short description of the model. Imagine that each vertex has k tokens. This suggests that we have in total kn tokens, where is the number of vertices and you can freely think of . Also, let me mention that […]
Martingales & Coins: Waiting for Heads-Tails-Heads
Consider the following simple problem: let be a sequence of independent fair coin tosses. How many times do we have to toss the coin in expectation in order to observe the sequence HTH (H stands for heads and T for tails)? We will answer this question here with three different ways. The first way is […]
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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