Lecture

Interlacing Family and Matrix Determinant Lemma

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MATH-467: Probabilistic methods in combinatorics

The 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...

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This lecture covers topics such as interlacing family, matrix determinant lemma, and mixed characteristics of random matrices. It also delves into the concept of laynen polynomials and their properties, providing insights into polynomial roots and determinants.

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