Скачать или смотреть CO14 Counting Permutations of a Set

#permutations are ordered lists or bijections from a set to itself. An s-permutation of [t]={1, 2, ..., t} is an ordered arrangement of s elements of [t] (assuming that s is no more than t). The number of s-permutations of [t] is (t)_s where the latter is a falling factorial. The number of s-permutations of [t] is also the same as the number of ways of placing s distinct balls into t distinct boxes in such a way that each box gets at most one ball. Examples of counting problems are given.
00:00 Introduction
00:13 What is a permutation?
01:22 Number of permutations of a set with n elements is n!
02:36 A permutation is a 1-1, onto function (   • GF1 What is a function? What do 1-1 and on...  )
03:54 What is a s-permutation?
04:22 Number of s-permutations of set with t elements
05:55 Example of a falling factor
06:36 Definition of falling factors
08:13 s-permutations translated to balls & boxes
12:19 The balls & boxes framework for counting (   • CO12 Balls & Boxes Counting Problems  )
14:15 Example: 13 people to be seated in a row but there are 5 of those 13 that cannot sit next to each other. In how many ways can this be done?
16:30 Placing non-attacking rooks on the chess board & permutations
18:11 Example: In how many ways can you place 8 distinct non-attacking rooks on an 8x8 chess board?

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 for Combinatorics see
https://pomona.box.com/s/by2ay2872avx...
YouTube 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.