Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The facial weak order and its lattice quotients
HTML articles powered by AMS MathViewer

by Aram Dermenjian, Christophe Hohlweg and Vincent Pilaud PDF
Trans. Amer. Math. Soc. 370 (2018), 1469-1507 Request permission

Abstract:

We investigate the facial weak order, 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 first provide three characterizations of this poset: the original one in terms of cover relations, the geometric one that generalizes the notion of inversion sets, and the combinatorial one as an induced subposet of the poset of intervals of the weak order. These characterizations are then used to show that the facial weak order is in fact a lattice, generalizing a well-known result of A. Björner 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 their classes. As application, we describe the facial boolean lattice on the faces of the cube and the facial Cambrian lattice on the faces of the corresponding generalized associahedron.
References
Similar Articles
Additional Information
  • Aram Dermenjian
  • Affiliation: LIX, École Polytechnique, Palaiseau & LaCIM, Université du Québec À Montréal (UQAM), Montréal, Québec H2H 2A9, Canada
  • Email: aram.dermenjian@gmail.com
  • Christophe Hohlweg
  • Affiliation: LaCIM, Université du Québec À Montréal (UQAM), Montréal, Québec H2H 2A9, Canada
  • MR Author ID: 685087
  • Email: hohlweg.christophe@uqam.ca
  • Vincent Pilaud
  • Affiliation: CNRS & LIX, École Polytechnique, Palaiseau, France
  • MR Author ID: 860480
  • Email: vincent.pilaud@lix.polytechnique.fr
  • Received by editor(s): February 16, 2016
  • Received by editor(s) in revised form: May 18, 2017
  • Published electronically: October 24, 2017
  • Additional Notes: The first author was partially supported by the French ANR grant EGOS (12 JS02 002 01) and an ISM Graduate Scholarship. The second author was supported by NSERC Discovery grant Coxeter groups and related structures. The third author was partially supported by the French ANR grants EGOS (12 JS02 002 01) and SC3A (15 CE40 0004 01).
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 1469-1507
  • MSC (2010): Primary 05E99, 20F55; Secondary 06B99, 03G10
  • DOI: https://doi.org/10.1090/tran/7307
  • MathSciNet review: 3729508