Mathematics Seminar
Date: Wednesday, 19 June 2024
Time: 10.30 AM
Venue: Seminar Hall
A bijective proof of a partition identity
Krishna Menon
Chennai Mathematical Institute.
19-06-24

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Abstract

A partition of a number is a way to write it as a sum of positive integers. One way to visualize a partition is as a certain stack of boxes called its Young diagram. There are several numbers one can associate to each box of a Young diagram. We will be discussing two such quantities: 'hook length' and 'content'. Hook lengths in particular are very popular in the world of partitions. There is an interesting formula that relates hook lengths and contents, which isn't too hard to prove via induction. However, as is the norm in combinatorics, one always prefers a bijective proof. In this talk, I will present such a proof, which solves a problem posed by Richard Stanley.

This talk is based on https://arxiv.org/abs/2403.05072