DOAJ Open Access 2014

Gallery Posets of Supersolvable Arrangements

Thomas McConville

Lihat Sumber DOI

Abstrak

We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of reduced words. Using Rambau's Suspension Lemma, we show that these posets are homotopy equivalent to spheres. We furthermore conjecture that its intervals are either homotopy equivalent to spheres or are contractible. One may view this as a analogue of a result of Edelman and Walker on the homotopy type of intervals of a poset of chambers of a hyperplane arrangement.

Topik & Kata Kunci

Mathematics

Penulis (1)

Thomas McConville

Format Sitasi

APA MLA BibTeX

McConville, T. (2014). Gallery Posets of Supersolvable Arrangements. https://doi.org/10.46298/dmtcs.2444

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2444

Informasi Jurnal

Tahun Terbit: 2014
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2444
Akses: Open Access ✓