Скачать или смотреть CO32 The Inclusion-Exclusion Principle

The statement, proof, and examples of the inclusion-exclusion principle in #combinatorics. How many integers between 1 and 10,000 are not divisible by 2, 3, or 5? How many permutations of M, A, T, H, I, S, F, U, N do not include MATH, IS, or FUN? How do you find the chromatic polynomial of a graph?
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00:00 Introduction
00:15 Addition Principle
01:00 Complements, Unions, Intersections
02:29 Inclusion-Exclusion for two sets
07:25 Inclusion-Exclusion Principle for m sets
10:57 Proof of the Inclusion-Exclusion Principle
14:05 Example: Number of integers between 1 and 10,000 that are not divisible by 2, 3, or 5
17:52 number of permutations of M, A, T, H, I, S, F, U, N that do not include MATH, IS, or FUN as consecutive letters
20:47 a special case of the I-E principle when the size of intersections is independent of the choice of sets & only depends on the number of involved sets
22:38 Application to finding the chromatic polynomial of a graph
Next Video:    • CO34 Combinations of Multisets via Inclusi...  

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A series of lectures on introductory Combinatorics. This full course is based on my book

Shahriar Shahriari, An Invitation to Combinatorics, Cambridge University Press, 2022.
DOI: https://doi.org/10.1017/9781108568708

For an annotated list of available videos on Combinatorics see
https://pomona.box.com/s/by2ay2872avx...

YouTube Combinatorics Playlist:    • Combinatorics, An Invitation  

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and six time winner of Pomona College's Wig teaching award.