Topics In Combinatorics Lecture 9

Sean explains why math is useful and talks about visualizing the Fibonacci sequence through

This is a graduate course that I taught at Sungkyunkwan University in 2017. We closely follow the book: Proofs and Confirmations ...

How large can a subset of the unit sphere of R^n be if it contains no pair of orthogonal vectors? The Frankl-Wilson theorem (in the ...

This is an introduction to the concept of entropy (in the information-theoretic sense of the word). In the next few videos I shall say ...

Let F be a family of subsets of {1,2,...,n} such that every set in F has size that satisfies some congruence condition mod p and every ...

Guest

Suppose you have n points and m lines in the plane. A point-line incidence is a pair (P,L) where P is one of the points and L is one ...

Having presented some (but by no means all) of the basic theory of entropy, I give an application to the following problem: let G be ...

We prove several partition identities, including Euler's pentagonal number theorem.

We say that a permutation pi of {1,2,...,k} is contained in a permutation sigma of {1,2,...,n} if we can find k elements of {1,2,...,n} that ...

In this video I present the formula for the entropy of a random variable that takes values in a finite set, prove that it satisfies the ...

Fundamental Counting Principle, Permutations, & Combinations Permutation formula: ...

MIT Student Explains All Of

In this video, I will show you the basics of combinations and permutations.

... symmetric group we know a lot beautiful forms beautiful

A result that has played a central role in additive

In the previous video I stated and proved Shearer's entropy lemma. Here I give two applications. The first provides an upper ...