RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

sponsored by the

Rutgers University
Department of Mathematics

and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Founded 2003 by Drew Sills and Doron Zeilberger.

Former co-organizers: Drew Sills (2003-2007), Moa ApaGodu (2005-2006), Lara Pudwell (2006-2008), Andrew Baxter (2008-2011), Brian Nakamura (2011-2013), Edinah Gnang (2011-2013), Matthew Russell (2013-2016), Nathan Fox (2016-2017), Bryan Ek (2017-2018), Mingjia Yang (2018-2020), Yonah Biers-Ariel (2018-2020)

Current co-organizers:
Doron Zeilberger (doronzeil {at} gmail [dot] com)
Robert Dougherty-Bliss (robert {dot} w {dot} bliss {at} gmail [dot] com)

Archive of Previous Speakers and Talks You can find links to videos of some of these talks as well. Currently, our videos are being posted to our Vimeo page. Previously, we had videos posted on our YouTube page.


If you would like to be added to the weekly mailing list, email Robert Dougherty-Bliss (robert {dot} w {dot} bliss {at} gmail [dot] com)

Forthcoming Talks



Spring 2021


Date: Jan. 28 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Victor S. Miller, Center for Communications Research, Princeton.

Title: Counting Matrices that are Squares

Abstract: On the math-fun mailing list (7 May 2013), Neil Sloane asked to calculate the number of n times n matrices with entries in {0,1} which are squares of other such matrices. In this paper we analyze the case that the arithmetic is in GF(2) We follow the dictum of Wilf (in the paper ``What is an answer?'') to derive a ``effective'' algorithm to count such matrices in much less time than it takes to enumerate them. The algorithm which we use involves the analysis of conjugacy classes of matrices. The restricted integer partitions which arise are counted by the coefficients of one of Ramanujan's mock Theta functions, which we found thanks to Sloane's OEIS (Online Encyclopedia of Integer Sequences).



Date: Feb. 4 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Ron Adin, Bar Ilan University, Israel.

Title: Cyclic permutations, shuffles, and quasi-symmetric functions

Abstract: Richard Stanley proved that the distribution of descent number over all the shuffles of two permutations depends only on the descent numbers of the permutations.

We present an explicit cyclic analogue of this result. The tools used for the proof include a new cyclic counterpart of Gessels quasi-symmetric functions, an unusual ring homomorphism, and a mysterious binomial identity with an interesting history.

Based on joint work with Ira Gessel, Vic Reiner, and Yuval Roichman.


Date: Feb. 11 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Colin Defant, Princeton University

Title: Cumulants and Stack-Sorting

Abstract: Cumulant sequences are numerical sequences that play a fundamental role in noncommutative probability theory. West's stack-sorting map is a combinatorially-defined operator that acts on permutations. In this talk, we will discuss how cumulants and stack-sorting, two topics from very disparate worlds, are actually very closely related. This unexpected connection allows us to use tools from noncommutative probability theory to prove difficult, surprising, and (occasionally) weird facts about the stack-sorting map. We will explore several applications of this method.


Date: Feb. 18 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Nathan Fox, Canisius College

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Date: Feb. 25 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: March 4 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: March 11 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
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Date: March 18 , 2020, 5:00pm (Eastern Time)

NO TALK DUE TO SPRING BREAK


Date: March 25 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: April 1 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: April 8 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: April 15 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: April 22 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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Date: April 29 , 2020, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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