Combinatorial relationships realized bijectively among such classes are transformed into functional relationships of their generating functions. For example, from the combinatorial interpretation of a set partition as a set of non-empty sets, the exponential generating function for Bell numbers exp(exp(z)-1) becomes blindingly clear; exp(z) is the generating function of sets and exp(z)-1 that of non-empty ones.
I will discuss species of structures and some generating functions that are associated with them. I will explain how algebraic operations on generating functions can be seen to arise from set-theoretic operations on species. I will introduce the Frobenius characteristic generating function of a species of structures, which is a simple variation of the cycle index generating function, landing us in the world of symmetric polynomials.
[maxbutton id=”1″ url=”https://ashoka.edu.in/static/doc_uploads/file_1631727563.pdf” text=”Lecture Slides” ]