This seminar will continue the study of the concepts related to enumerative combinatorics and discrete structures related to the class Discrete Mathematics 1. Depending on interest, it will cover various topics among the follow:
- Algebraic Methods (Group theory, Symmetric Group, Group actions, Polya Theory, Holonomic sequences, Hypergeometric sequences),
- Generating Functions (Polynomials, Quasi-polynomials, Transfer-matrix method, Basics of species)
- Facial enumeration of simplicial complexes (Kruskal-Katona and Frankl-Furedi-Kalai Theorems),
- Embedding of graphs and simplicial complexes (van Kampen-Flores Theorem),
- Poset and Lattice theory (Tarski's Fixed Point Theorem, Boolean Algebras, Fundamental Theorem of Finite Distributive Lattices, Galois connection theorems),