Cornell Math - MATH 735, Fall 2005
MATH 735: Introduction to Enumerative Combinatorics (Fall 2005)
Instructor: Edward Swartz
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 as Hilbert functions of algebraic objects, and the influence of topological properties on both.
We will assume only a basic knowledge of linear algebra and ring theory (say at the level of MATH 433-434) and will develop the necessary ideas from commutative algebra and topology as they are needed.
Much (but not all) of what we will do can be found in Stanley's book Enumerative Combinatorics, Vol. I (Cambridge, 1997).