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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.