CO15 Circular Permutations, # of k-cycles in S_n скачать в хорошем качестве

CO15 Circular Permutations, # of k-cycles in S_n

Circular Permutations, r-circular #permutations of [n], and k-cycles of S_n are defined, and counted. Examples given. In a circular permutation, only the relative position of objects matter. How many ways can you seat 47 people around a round table assuming the actual seats are identical and what only matters is the relative position of the individuals? #combinatorics Subscribe ‪@Shahriari‬ for math videos at the college level. 00:00 Introduction 00:24 Motivating Problem: From among a group of 7 people, in how many ways can you seat 4 of them around a round table? 01:38 Definition: circular permutations 04:49 r-permutations (   • CO14 Counting Permutations of a Set  ) 06:49 counting circular r-permutations 10:13 Problem: Two groups of 4 and you (for a total of 9) to be seated around a round table with no two persons from the same group next to each other. In how many ways can this be done? 13:53 S_n, the symmetric group, and cycle notation (   • AG04 What is the Symmetric Group S_n? Cycl...  ) 16:07 Number of k-cycles in S_n 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 five time winner of Pomona College's Wig teaching award.