Math 6310: Topics in Combinatorics
Instructor: Professor Joseph Kung
MW 12:00 - 1:20
This will be a course on algebraic and enumerative combinatorics. The focus will be on counting and homology in partially ordered sets and lattices. We will start with basic counting methods: what to do when you meet an integer sequence, recursions, generating functions, the standard counting numbers, and using databases like OEIS [online encyclopedia of integer sequences] . More advanced topics include Moebius functions, characteristic polynomials, chain and no-broken-circuit complexes. We will also study specific examples: subspace and subgroup lattices, lattices of intersections of arrangements of hyperplanes, Bruhat orders, and permutahedrons. We will definitely not be doing CATegory theory.
We will not have an official textbook, but a useful reference is R. Graham, D. Knuth, and O.Patashnik, Concrete Mathematics, Addison-Wesley, 1989, 0-201-14236-8.
View the Course Descriptions from the University Catalog