probmethod_notes.pdf

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Lecture notes (MIT 18.226, Fall 2020) Probabilistic Methods in Combinatorics Yufei Zhao Massachusetts Institute of Technology yufeiz@mit.edu http://yufeizhao.com/pm/ Contents 1 Introduction 1 1.1 Lower bounds to Ramsey numbers . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Erdős’ original proof . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Alteration method . . . . . . . . . . . . . . . . . . .…

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