Loading...
Please wait, while we are loading the content...
Similar Documents
Flag Enumeration in Polytopes, Eulerian Partially Ordered Sets and Coxeter Groups
| Content Provider | Semantic Scholar |
|---|---|
| Author | Billera, Louis J. |
| Copyright Year | 2011 |
| Abstract | We discuss the enumeration theory for ags in Eulerian partially ordered sets, emphasizing the two main geometric and algebraic examples, face posets of convex polytopes and regular CW -spheres, and Bruhat intervals in Coxeter groups. We review the two algebraic approaches to ag enumeration { one essentially as a quotient of the algebra of noncommutative symmetric functions and the other as a subalgebra of the algebra of quasisymmetric functions { and their relation via duality of Hopf algebras. One result is a direct expression for the Kazhdan-Lusztig polynomial of a Bruhat interval in terms of a new invariant, the complete cd-index. Finally, we summarize the theory of combinatorial Hopf algebras, which gives a unifying framework for the quasisymmetric generating functions developed here. |
| Starting Page | 2389 |
| Ending Page | 2415 |
| Page Count | 27 |
| File Format | PDF HTM / HTML |
| DOI | 10.1142/9789814324359_0151 |
| Alternate Webpage(s) | http://www.math.cornell.edu/~billera/papers/eulericm.pdf |
| Alternate Webpage(s) | http://www.math.cornell.edu/~billera/lectures/ICMbillera.pdf |
| Alternate Webpage(s) | http://www.mathunion.org/ICM/ICM2010.4/Main/icm2010.4.2389.2415.pdf |
| Alternate Webpage(s) | https://doi.org/10.1142/9789814324359_0151 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
