Submaximal factorizations of a Coxeter element in complex reflection groups
Abstrak
When $W$ is a finite reflection group, the noncrossing partition lattice $NC(W)$ of type $W$ is a very rich combinatorial object, extending the notion of noncrossing partitions of an $n$-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in $NC(W)$ as a generalized Fuß-Catalan number, depending on the invariant degrees of $W$. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of $NC(W)$ as fibers of a "Lyashko-Looijenga covering''. This covering is constructed from the geometry of the discriminant hypersurface of $W$. We deduce new enumeration formulas for certain factorizations of a Coxeter element of $W$.
Topik & Kata Kunci
Penulis (1)
Vivien Ripoll
Akses Cepat
- Tahun Terbit
- 2011
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2955
- Akses
- Open Access ✓