Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Journal of the Europ...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Journal of the European Mathematical Society
Article . 2009 . Peer-reviewed
Data sources: Crossref
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 2009
Data sources: zbMATH Open
https://dx.doi.org/10.48550/ar...
Article . 2006
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
versions View all 5 versions
addClaim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

Cambrian fans

Cambrian fans.
Authors: Nathan Reading; David E. Speyer;
Abstract

For a finite Coxeter group W and a Coxeter element c of W, the c -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of W\! . Its maximal cones are naturally indexed by the c -sortable elements of W\! . The main result of this paper is that the known bijection \operatorname{cl}_c between c -sortable elements and c -clusters induces a combinatorial isomorphism of fans. In particular, the c -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for W\! . The rays of the c -Cambrian fan are generated by certain vectors in the W -orbit of the fundamental weights, while the rays of the c -cluster fan are generated by certain roots. For particular (“bipartite”) choices of c , we show that the c -Cambrian fan is linearly isomorphic to the c -cluster fan. We characterize, in terms of the combinatorics of clusters, the partial order induced, via the map \operatorname{cl}_c , on c -clusters by the c -Cambrian lattice. We give a simple bijection from c -clusters to c -noncrossing partitions that respects the refined (Narayana) enumeration. We relate the Cambrian fan to well known objects in the theory of cluster algebras, providing a geometric context for \mathbf{g} -vectors and quasi-Cartan companions.

Keywords

cluster algebras, maximal cells, Primary 20F55; Secondary 16S99, \(c\)-sortable elements, combinatorial isomorphisms of fans, Cambrian lattices, Cluster algebras, generalized associahedra, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Combinatorial aspects of groups and algebras, Combinatorics of partially ordered sets, finite Coxeter groups, Secondary 16S99, Reflection and Coxeter groups (group-theoretic aspects), Primary 20F55, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    38
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
38
Top 10%
Top 10%
Top 10%
Green
gold