CO31 Ferrers (aka Young) Diagrams for partitions of integers скачать в хорошем качестве

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.