Saturday April 13, 2024

Hosted by 

Hofstra University

New York Combinatorics Day is held at different locations in and around New York City. 
Our goal is to provide a learning and sharing experience on recent developments in Combinatorics.
Please encourage your students to attend and present a poster.

Location: Hofstra University C. V. Starr Hall, Room 210. It is building 60 on this campus map (or search for "C. V. Starr" in Google Maps).

Registration:  There is no registration fee and lunch is free, however, for logistics please register online by filling this Registration Form by April 11, 2024. 

Keynote Speakers: Deepak Bal, Anna Pun, and Zoran Sunik

Schedule (in Eastern Time ET)

10:30 am - 11:00 pm:  Check-In/Coffee

11:00 am - 12:00 pm:  Deepak Bal (Montclair State University)

12:00 - 1:00 pm: Lunch and Poster Session

1:00 pm - 2:00 pm:   Anna Pun (Baruch College, CUNY)

2:00 - 2:15 pm: Break

2:15 - 3:15 pm: Zoran Sunik (Hofstra University)

Abstracts

Deepak Bal (Montclair State University)

Title: Multicolor Ramsey Numbers of Double Stars

Abstract: The balanced double star on 2n+2 vertices, denoted S(n,n), is the tree obtained by joining the centers of two disjoint stars each having n leaves. Let R(G;r) be the smallest integer N such that in every r-coloring of the edges of K_N there is a monochromatic copy of G, and let B(G;r) be the smallest integer N such that in every r-coloring of the edges of K_{N,N} there is a monochromatic copy of G.  R(S(n,n);2) and B(S(n,n);2) are known, but very little is known about R(S(n,n);r) and B(S(n,n);r) when r >= 3. We prove new bounds for these cases. 

Anna Pun (Baruch College)

Title: The magic of tableaux: exploring the wonders of algebraic combinatorics
Abstract: Tableaux are one of the most fundamental and versatile objects in algebraic combinatorics, as they can encode and connect various concepts and structures in the field. In this talk, we will start with the definition and properties of Young tableaux, which are graphical representations of partitions of integers. We will then see how tableaux can be used in algebra: their connection to symmetric functions and partition algebras; how they can be related to various combinatorial operations, such as the RSK-algorithm and the Jeu-de-taquin procedure; and how they can give rise to various combinatorial structures, such as lattice paths, vacillating tableaux, and parking functions. We will also explore some variations of tableaux, such as composition tableaux and set-valued tableaux, and discuss some interesting problems and conjectures that arise from them. We will conclude with some open questions and directions for future research on tableaux and their applications in algebraic combinatorics.

Zoran Sunik (Hofstra University)
Title: Counting trees with(out) properties
Abstract: It is well known that the (planar) rooted binary trees with given number of leaves are counted by the Catalan numbers. It is also well known that such binary trees are related to well-balanced patterns of parentheses, as used in algebra. We present solutions to several counting problems in the similar vein, where algebraic problems related to various identities are directly reduced to counting binary trees that avoid certain patterns. Note that our solutions are not explicit and are given in form of recursions and equations satisfied by the corresponding generating functions. For instance, the generating function F(z) counting the algebraic expressions with single variable and single binary operation that avoid any pattern of the form (AA)A satisfies the equation F(z) = z + F(z)^2 - F(z^3).

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Directions to Hofstra University: To get to Hofstra using public transportation, take the Long Island Railroad from Penn Station or Grand Central Station to Mineola; train times are available here. From Mineola, Hofstra operates a free shuttle. Go to shuttle schedule and click “Train shuttle Sat./Sun." in the table. Alternatively, take the Long Island Railroad to Hempstead and take the shuttle from there, although trains to Hempstead are less frequent. Get off the shuttle at the Student Center (stop number 2 on this map) since the shuttle doesn’t stop on the south half of campus over the weekend. Enter the Student Center, and then keep walking straight to cross the unispan over Hempstead Turnpike. Then make your way to C. V. Starr Hall.

Parking at Hofstra University: Anyone can park in Faculty/Staff lots on weekends. Lots 2B and 2C on this map are close to C. V. Starr Hall.

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There is a place to upload your poster title on the registration form. If you have any questions about the poster session, please email Dr. Sandra Kingan (skingan@brooklyn.cuny.edu). For information on registration and logistics contact Dr. Eric Rowland (eric.rowland@hofstra.edu).

Local Organizing Committee at Hofstra University: Kira Adaricheva, Eric Rowland, Sylvia Silberger, Zoran Sunik.