CO30 Integer Partitions

#combinatorics In how many ways can you put 10 identical balls in 4 piles? Each possibility is a partition of the integer 10 into 4 non-empty parts and the total number is denoted by p_k(n). We will give definitions, examples, and two recurrence relations (with proof) for p_k(n). Subscribe ‪@Shahriari‬ for math videos at the college level.
00:00 Introduction
00:11 Partitions of 7 into 2 parts
01:04 Definition: Partitions of an integer
02:21 Example: p_2(4)
04:01 Easy cases
04:39 Balls & Boxes
06:10 Recurrence relation for p_k(n)
09:35 A second recurrence relation
11:08 Table of small values of p_k(n) and p(n)
Next Video on partitions:    • CO31 Ferrers (aka Young) Diagrams for part...  

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.