Date: Thu., Jan. 18, 2024, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:Neil Sloane, The OEIS Foundation and Rutgers University-
Title: Eric Angelini's Comma Sequence
Abstract: The Comma Transform of a sequence replaces each comma between the terms by the number formed by concatenating the single digits to the left and right of the comma. (E.g., the Comma Transform of the even numbers is 2, 24, 46, 68, 81, 1, ....) The remarkable "comma sequence" is defined by the property that it starts with 1 and its first differences equal its Comma Transform. If there is a choice, choose the smallest possibility. It contains exactly 2137453 terms! This talk, based on joint work with Eric Angelini, Michael Branic ky, Giovanni Resta, and David W. Wilson, will analyze this and related sequences.
Date: Thu., Feb. 1, 2024, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:
George Spahn, Rutgers University
Title: Counting Maximal Seat Assignments that obey Social Distancing
Abstract: If I'm proctoring an exam and write on the board that students may not sit adjacent to another student, what should I expect the density of students to be in the seats? We analyze this question by counting maximal arrangements and then show how to generalize the method to answer other related questions. (Joint work with Doron Zeilberger).
Date: Thu., Feb. 15, 2024, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:
Peter Olver, University of Minnesota
Title: Allen Tannenbaum and Computer Vision
Abstract: I will present some of the late Allen Tannenbaum's fundamental contributions to image processing and computer vision, concentrating on our collaborative research. Topics include use of symmetry groups and nonlinear partial differential equations, image denoising and segmentation, and differential invariant signatures for object recognition and symmetry detection, including invariant numerical schemes and later applications to jigsaw puzzles, broken bone assembly, and cancer detection
Date: Thu., Feb. 29, 2024, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:
Jesús Guillera, University of Zaragoza
Title: Bilateral rational Ramanujan series and their p-adic mates
Abstract: We conjecture p-adic identities associated to bilateral rational Ramanujan-like series. Then, we show how to recover the rational Ramanujan series from their p-adic mates
Date: Thu., March 7, 2024, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: AJ Bu, Rutgers University
Title: Studying the Area under (Generalized) Dyck Paths
Abstract: I will be presenting my work (along with some joint work with Doron Zeilberger) on how to use symbolic computation to study the area under generalized Dyck paths (i.e. paths in the xy-plane from the origin to (n,0) with an arbitrary set of atomic steps and that never go below the x-axis).
Date: Thu., March 28, 2024, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:
Adam Zsolt Wagner, Worcester Polytechnic Institute.
Title: Reinforcement learning and pattern finding in combinatorics
Abstract: We will look at two ways we can use tools from machine learning to help us with research in combinatorics. First we discuss reinforcement learning, a method that gives us a way to check conjectures for counterexamples efficiently. While it usually does not perform as well as other simpler methods, there have been several examples of projects in the past few years where RL was crucial for success. In the second half of the talk we will consider the following question of Ellenberg: at most how many points can we pick in the N by N grid, without creating an isosceles triangle? The best known constructions, found by computer searches for small values of N, clearly follow a pattern which we do not yet understand. We will discuss how one can train transformers to understand this pattern, and use this t rained transformer to help us find a bit better constructions for various N. This is joint work with Jordan Ellenberg, Marijn Heule, and Geordie Williamson
Date: Thu., April 11, 2024, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: Natalya Ter-Saakov, Rutgers University
Title: Eric Angelini's Comma Sequence Part 2
Abstract: At the beginning of the semester, Neil Sloane introduced the comma sequence (introduced to him by Eric Angelini) that works as follows. Choose your favorite number in your favorite base. Now we'll build a sequence from it with the following rule: the difference between consecutive terms is equal to the concatenation of the digits on either side of the comma between them. If you chose 1 and base 10, then your next terms would be 12 because 12-1=11 and then 35 because 35-12=23. This sequence will continue for 2,137,452 steps, then fails to find a suitable successor for the value 99,999,945. We will discuss some problems presented by Sloane including a proof that all comma sequences in bases 3 through 19 are finite. Based on joint work with Robert Dougherty-Bliss.
Date: Thu., April 25, 2024, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:
Eugene Zima, Wilfrid Laurier University
Title: Effectively multiplication- and division-free residue number systems
Abstract: Several methods of selection of moduli in modular arithmetic are considered. With the proposed choice of moduli both modular reduction of an integer and reconstruction from modular images are accelerated. Special attention is paid to the moduli of the forms 2n ± 1 and 2n ± 2k ± 1. Different schemes of choice of these types of moduli and algorithms for conversion of arbitrary precision integers into the modular representation and back are considered. Results of experimental implementation of a two-layer modular arithmetic in GMP system are discussed.