DOAJ Open Access 2020

The facial weak order in finite Coxeter groups

Aram Dermenjian Christophe Hohlweg Vincent Pilaud

Lihat Sumber DOI

Abstrak

We investigate a poset structure that extends the weak order on a finite Coxeter group W to the set of all faces of the permutahedron of W. We call this order the facial weak order. We first provide two alternative characterizations of this poset: a first one, geometric, that generalizes the notion of inversion sets of roots, and a second one, combinatorial, that uses comparisons of the minimal and maximal length representatives of the cosets. These characterizations are then used to show that the facial weak order is in fact a lattice, generalizing a well-known result of A. Bjo ̈rner for the classical weak order. Finally, we show that any lattice congruence of the classical weak order induces a lattice congruence of the facial weak order, and we give a geometric interpretation of its classes.

Topik & Kata Kunci

Mathematics

Penulis (3)

Aram Dermenjian

Christophe Hohlweg

Vincent Pilaud

Format Sitasi

APA MLA BibTeX

Dermenjian, A., Hohlweg, C., Pilaud, V. (2020). The facial weak order in finite Coxeter groups. https://doi.org/10.46298/dmtcs.6399

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6399

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6399
Akses: Open Access ✓