CO31 Ferrers (aka Young) Diagrams for partitions of integers

#combinatorics Ferrers (aka Young) diagrams help visually to discover and prove theorems about partitions of an integer. Two #recurrencerelations and two theorems are proved: (1) a bijection between partitions of n into k parts and partitions of n (into any number of parts) where the largest part is k, and (2) a bijection between self-conjugate partitions of n and partitions of n into odd distinct parts. Subscribe ‪@Shahriari‬ for math videos at the college level.
00:00 Introduction
00:12 Partitions of an integer and partition numbers (   • CO30 Integer Partitions  )
01:16 Ferrers Diagrams (aka Young Diagrams)
02:07 Recurrence relations via Ferrers Diagrams
05:06 Table of Small Values for p_k(n) & p(n)
05:29 Conjugate Partitions
06:40 Partitions of 6 into 3 parts and their conjugates
07:37 Theorem: p_k(n) = number of partitions of n into any number of parts where the largest part is k
08:22 Self-Conjugate Partitions
08:56 Proof and Theorem: # of self conjugate partitions of n equals the # of partitions of n into distinct odd parts

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.