Скачать или смотреть CO44 Examples of Posets in Combinatorics

#combinatorics Partitions of a set (ordered by refinement) and partitions of an integer (ordered by dominance) as well as the collection of all independent sets of vertices of a #graph all form posets. These and subsets of a finite set and divisors of an integer are given as examples of partially ordered sets (aka posets) in Combinatorics. #graphtheory Subscribe ‪@Shahriari‬ for math videos for college students.

00:00 Introduction
00:21 Definition: Poset
01:53 Example: Boolean Lattices
02:26 Comparability & Cover Relations
03:31 Definition: Hasse Diagram
04:04 Hasse diagram of Boolean Lattices
04:31 Hasse diagram of integers and divisors of an integer
04:54 Poset of Partitions of a set ordered by refinement
07:25 Poset of Partitions of an integer ordered by dominance
09:18 Poset of independent sets (ordered by inclusion) in a graph

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.