Lecture

Ramanujan Graphs: Constructions and Similarities

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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 ...

Description

This lecture covers the constructions and similarities of Ramanujan graphs, focusing on the matching polynomials and perfect matchings. The instructor explains the building methods and the high probability choices involved. The lecture also delves into the differences between group theory and Ramanujan graphs, highlighting open problems in the field. Additionally, the concept of random walks on universal covers is discussed, along with the theory of expected characteristic polynomials. The lecture concludes with a detailed exploration of quantitation and qualitative aspects, emphasizing the challenges and functions related to soft matrices and root calculations.

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Visual arts: Painting

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