Annual Seminar for Mathematics Research Scholar Date: Thursday, 19 October 2023 Time: 3:30 PM Venue: Seminar Hall An introduction to the exponential formula in combinatorics Krishna Menon Chennai Mathematical Institute. 191023 Abstract There are several ways that one can give structure to a finite set. One may impose the structure of a graph, permutation, partition, etc. In this talk, I will be focused on the problem of describing the number of ways one can give a particular structure to a finite set. One way to attempt this problem is using a tool called "Exponential Generating Functions" (EGFs). I will discuss the correspondence between algebraic operations on these EGFs and combinatorial operations on structures. I will also present several concrete examples. For instance, I will show how to prove: log(EGF for graph structures) = EGF for connected graph structures.
