# Seminars & Colloquia Calendar

## How Prolific is a Random Permutation?

#### Peter Winkler (Dartmouth College)

Location: ** Hill 705**

Date & time: Monday, 24 February 2020 at 2:00PM - 3:00PM

Abstract:

A "pattern" of length k in a permutation \(P\) in \(S_n\) is a permutation in \(S_k\) determined by choosing \(k\) elements from {1,2,...,n} and looking at the order of their images under \(P\). For example, if \(P_3 > P_5\) then the positions 3 and 5 produce the pattern 21.

\(P\) is "\(d\)-prolific" if every pattern of length n-d is different; equivalently, the set of patterns of \(P\) of length \(n-d\) has size \(n\) choose \(d\).

We show that the probability that a uniformly random \(P\) in \(S_n\) is \(d\)-prolific tends to \(e^{-d^2-d}\) as \(n\) grows.

Joint work with Simon Blackburn and Cheyne Homberger.

R. Shapiro Organizer's Page

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

Organizer's webpage: Organizer's webpage

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