I will use the material from a paper by Shai Simonson and Tara S. Holm. This is part of their abstract:
We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory.
We give a survey on connections between Graph Isomorphism, the CSP, and counting homomorphisms. In the first part we give a brief review of the main approaches to solving the Graph Isomorphism problem and make some observations on how the CSP techniques can be helpful. In the second part we focus on relaxations of graph isomorphisms and how they can be characterized using the numbers of homomorphisms from various graph classes.
This talk is based on joint work with M.Khovanov and Y.Kononov. By evaluating a topological field theory in dimension 2 on surfaces of genus 0,1,2 etc we get a sequence. We investigate which sequences occur in this way depending on the assumptions on the target category.
Two dimensional topological field theories and partial fractions