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About Three Tutorial Lectures
This document summarizes three tutorial lectures on using entropy as a tool for counting and enumeration problems in combinatorics. It begins by defining entropy for discrete random variables and deriving some of its basic properties, including subadditivity and Shearer's lemma. It then provides four quick examples of how entropy can be applied to counting problems involving sums of binomial coefficients, coin weighing problems, the Loomis-Whitney theorem, and intersecting families. The document continues with more in-depth examples involving embedding graphs, Brégman's theorem on matrix permanents, and counting graph homomorphisms. It concludes with some open problems related to counting matchings and graph homomorphisms.
Detailed Information
| Author: | ['Raina Wang'] |
|---|---|
| Publication Year: | 2019 |
| Pages: | 36 |
| Language: | English |
| Format: | |
| Price: | FREE |
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