MATH 739: Enumerative Combinatorics (spring 2008)

Instructor: Edward Swartz

Meeting Time & Room

A general introduction to algebraic combinatorics with a particular emphasis on methods of enumeration in ordered and geometric structures (partially ordered sets, simplicial complexes and polytopes).

Possible topics include (but are not limited to):

• Permutations and partitions,
• Partially ordered sets (posets) and lattices,
• Möbius inversion (inclusion-exclusion over posets),
• Posets as topological objects,
• Geometric lattices, including their relationship to hyperplane arrangements,
• Generating functions of combinatorial objects such as Hilbert functions of face rings, and the influence of geometric/topological properties on both.

We will assume only a basic knowledge of linear algebra and ring theory (say at the level of Math 433-4) and will develop the necessary ideas from commutative algebra and topology as they are needed.

About 2/3 of what we will do can be found in Stanley's book Enumerative Combinatorics, Vol. I (Cambridge, 1997).