The classical Frobenius problem asks for the largest integer not representable as a non-negative integer linear combination of a relatively prime integer n-tuple. This problem and its various generalizations have been studied extensively in combinatorics, number theory, algebra, theoretical computer science and probability theory. In this talk, we will consider a reformulation of this problem […]

In Euclidean geometry, the sum of  two sides of any  triangle is greater than the third side. We  introduce this idea to labeling of graphs. A (p,q)-graph G=(V,E) is said to be in Euclid(0) if there exists a bijection f: V(G) --> {1,…,p} such that for each induced C3 subgraph with vertices {v1,v2,v3} with f(v1)<f(v2)<f(v3) we […]

An “Adinkra” is a graphical tool to describe a branch of particle physics known as supersymmetry. Understanding the mathematics of Adinkras shines a light on the underlying physics, as well as helps to explore new areas of mathematics. After describing the basic structure of Adinkras, I will discuss some of these interesting interactions between mathematics […]

The classical, one-boundary, and two-boundary Temperley-Lieb algebras arise in mathematical physics related to solving certain rectangular lattice models.They also have beautiful presentations as "diagram algebras", meaning that they have basis elements depicted as certain kinds of graphs, and multiplication rules are given by stacking diagrams and gluing of vertices. In this talk, we will explore […]