Classes
Mondays 4:00-6:00 pm room A204 and Wednesdays 4:00-6:00 pm room N101.Literature
Enumerative combinatorics. Vol. I second edition. Cambridge University Press, 2012. Richard P. Stanley.Poset topology: tools and applications.arXiv preprint math/0602226, 2006. Michelle L Wachs.
Course content
The notion of order is a fundamental idea that is pervasive across almost every subject in mathematics. The formal study of partially ordered sets (posets) can be traced back to the nineteenth century but it had its major development in the twentieth century after the work of Birkhoff, among others, in lattice theory; Weisner, Hall and Ward in the theory of Möbius functions; and the seminal work of Gian-Carlo Rota in 1964 that gave the foundation to what is known today as poset topology, a field that studies interactions between poset theory, topology, algebra and enumeration.Grade distribution
Tests (30%)
There will be 2 tests. These will be announced at least one week in advance.Final project and presentation(30%)
Homework(40%)
There will be a set of problems to be handed in every two weeks. To work on the homework problems is crucial for your understanding of the material presented in class. Be sure to separate enough time each week to think and write your solutions. It is recommended that you think and attempt every problem on your own before seeking any help. You are encouraged to discuss the material of the course with your classmates, however you must write your own solutions using your own words.Problem Sessions
There will be various in-class problem sessions during the semester whose goal is to reinforce the concepts learned during a given week. During the problem sessions you are strongly encouraged to share what you have learned and to learn from your fellow class mates (share and learn).Suggested problems
There will be some additional suggested problems. These problems will be assigned after some of the classes and also posted in the web page of the course.Syllabus
| Tema |
|---|
| Basic Concepts |
| New Posets from Old |
| Lattices |
| Distributive Lattices |
| Chains in Distributive Lattices |
| Incidence Algebras |
| The Móbius Inversion Formula |
| Techniques for Computing Móbius Functions |
| Lattices and Their Móbius Functions |
| Hyperplane Arrangements |
| Zeta Polynomials |
| Rank Selection |
| R-labelings |
| Order complexes and poset topology |
| Poset homology and cohomology |
| Shellability and edge labelings |