Friday March 21, 2025

Hosted by 

CUNY Graduate Center

New York Combinatorics Day is held once a year at the Graduate Center, CUNY
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: CUNY Graduate Center, 4th floor Science Room, 365 Fifth Avenue (at the corner of 34th Street and 5th Avenue) in Manhattan across from the Empire State Building.  The entrance is on 34th street and the Science Center is on the 4th floor.  

Registration:  There is no registration fee. However, please fill out the registration form since there are room capacity limitations.  The form has space to enter poster information. 

Schedule (in Eastern Time ET)

10:00 am:  Check-In 

10:30 am:  Eric Ramos (Stevens Institute of Technology)

11:30 am: Rishi Nath (York College, CUNY)

12:30 am - 1:00 pm:  Lunch (8th floor cafeteria)

1:00 pm - 2:15 pm: Poster Session

2:15 pm:  Zhanar Berikkyzy (Fairfield University)

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Abstracts

Eric Ramos (Stevens Institute of Technology) 

Title: Universality theorems for generalized splines 

We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. We prove a finite generation result in this context, which implies a kind of universality in the generating set for the module of splines over any graph within a fixed homotopy class. Importantly, these results hold over any Noetherian commutative ring with a chosen finite list of ideals for edge-labels. One can think of our results as expanding upon and explaining many results about generating sets of the module of generalized splines. 

Rishi Nath (York College, CUNY)

Title: Core Connections: Partitions in Combinatorics, Number Theory and Representation Theory

Abstract: t-core partitions for positive integers t first arose in the study of the representation theory of the symmetric group. Since then, researchers have found connections between certain core partitions and modular forms, Dyck paths and parking functions. Here we survey important results in this field and highlight new and open problems.

Zhanar Berikkyzy (Fairfield University)

Title: Rainbow numbers of graphs and equations
Abstract: The rainbow number of a set of integers X for a given equation eq is the smallest number of colors r such that every exact r-coloring of X admits a rainbow solution to the equation eq. During this talk, we will discuss this number for several important equations, including Schur's and Sidon equations. We will then consider this parameter in graph setting and connect it to the anti-van der Waerden number of a graph, the fewest number of colors needed to guarantee a rainbow 3-term arithmetic progression. We will survey recent results for various classes of graphs, including trees and products of trees.

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Poster Session (1:00 - 2:00 pm)

There is a place to enter poster title and abstract on the registration form. Please bring your poster with you on the day of the event. If you have any questions about the poster session, email Profesor Kingan (skingan@brooklyn.cuny.edu).

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New York Combinatorics Day Steering Committee:
Kira Adaricheva, Sandra Kingan, Anna Pun, Abigail Raz, Eric Rowland