## RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

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

Date: April 8 , 2021, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Eric Sundberg, Occidental College

Title: Pairing Strategies for Tic-Tac-Toe on the Boolean Hypercube

Abstract: We consider a tic-tac-toe-style game on the vertices of the n-dimensional Boolean hypercube {0,1}n with k-dimensional subcubes as winning sets. We describe a pairing strategy which allows the second player to force a draw when k = n/4 +1 in the case where n is a power of 4. Our results arose from significant experimentation using Mathematica.
(Based on joint work with Klay Kruczek and Ramin Naimi)

Date: April 15 , 2021, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Igor Pak, UCLA.

Title: What is a combinatorial interpretation

Abstract: The question in the title is deceptively simple, as the answers tend to be the number of certain trees, lattice paths, Young tableaux, and other friendly combinatorial objects. However, the question lies in the heart of connections between enumerative/algebraic combinatorics and computer science. I will survey what is known about the subject, and discuss some of my recent results.

Date: April 22 , 2021, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Toufik Mansour, University of Haifa

Title: On Stanley-Wilf limit of the pattern 1324

Abstract: We present an explicit formula for the generating function for the number of permutations of length $n$ that avoid 1324 in terms of generating functions for permutations that have a kernel shape of length m, m ≥2. This allows us to write down a systematic procedure for finding a lower bound for approximating the Stanley-Wilf limit of the pattern 1324.
Joint work with Christian Nassau

Date: April 29 , 2021, 5:00pm (Eastern Time) Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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

Title: Locality preserving hash functions, a partial order and tiles in binary space

Abstract: A "tile" in the space B^n of bit vectors of length n, is a subset S of B^n, such that there is another subset A of B^n so that every element of B^n can be written uniquely in the form a + s, where a in A and s in S. A particular class of tiles are the subsets of minimum weight elements in the cosets of a linear code over GF(2). In systematically investigating locality preserving hash functions, we generated the list of all possible tiles of cardinality <=64 satisfying a certain optimality condition. All but 6 of them turned out to be the sets of minimum weight elements described above. Attempts to prove the same for the remaining 6 remained elusive. Instead we found two computational criteria -- one using linear programming, and the other using combinatorial bin packing, which showed that the remaining 6 could not be tiles.

[Joint with Don Coppersmith, Dan Gordon and Peter Ostapenko]