Skip to main content
Log in

Sortable elements and Cambrian lattices

  • Published:
Algebra universalis Aims and scope Submit manuscript

Abstract.

We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received December 22, 2005; accepted in final form March 19, 2006.

The author was partially supported by NSF grants DMS-0202430 and DMS-0502170.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reading, N. Sortable elements and Cambrian lattices. Algebra univers. 56, 411–437 (2007). https://doi.org/10.1007/s00012-007-2009-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00012-007-2009-1

2000 Mathematics Subject Classification:

Navigation