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Cambrian fans

Nathan Reading, David E. Speyer (2009)

Journal of the European Mathematical Society

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 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...

Chains, subwords, and fillings: strong equivalence of three definitions of the Bruhat order.

Zara, Catalin (2006)

The Electronic Journal of Combinatorics [electronic only]

Climbing elements in finite Coxeter groups.

Brady, Thomas, Kenny, Aisling, Watt, Colum (2010)

The Electronic Journal of Combinatorics [electronic only]

Combinatorial analysis of magnetic configurations.

Florek, W., Lulek, T. (1991)

Séminaire Lotharingien de Combinatoire [electronic only]

Combinatorial topology and the global dimension of algebras arising in combinatorics

Stuart Margolis, Franco Saliola, Benjamin Steinberg (2015)

Journal of the European Mathematical Society

In a highly influential paper, Bidigare, Hanlon and Rockmore showed that a number of popular Markov chains are random walks on the faces of a hyperplane arrangement. Their analysis of these Markov chains took advantage of the monoid structure on the set of faces. This theory was later extended by Brown to a larger class of monoids called left regular bands. In both cases, the representation theory of these monoids played a prominent role. In particular, it was used to compute the spectrum of the...

Completeness conditions in certain Weyl complexes, combinatorics and parsimony.

Sano, Mari (2005)

Boletín de la Asociación Matemática Venezolana

Computing Kazhdan-Lusztig polynomials for arbitrary Coxeter groups.

du Cloux, Fokko (2002)

Experimental Mathematics

Construction of Mendelsohn designs by using quasigroups of $(2, q)$ -varieties

Lidija Goračinova-Ilieva, Smile Markovski (2016)

Commentationes Mathematicae Universitatis Carolinae

Let $q$ be a positive integer. An algebra is said to have the property $(2, q)$ if all of its subalgebras generated by two distinct elements have exactly $q$ elements. A variety $𝒱$ of algebras is a variety with the property $(2, q)$ if every member of $𝒱$ has the property $(2, q)$ . Such varieties exist only in the case of $q$ prime power. By taking the universes of the subalgebras of any finite algebra of a variety with the property $(2, q)$ , $2 < q$ , blocks of Steiner system of type $(2, q)$ are obtained. The stated correspondence between Steiner...

Constructions of representations of rank two semisimple Lie algebras with distributive lattices.

Alverson II, L. Wyatt, Donnelly, Robert G., Lewis, Scott J., Pervine, Robert (2006)

The Electronic Journal of Combinatorics [electronic only]

Correspondences between the different types of bijections between the symmetric group and the valued Motzkin paths. (Correspondances entre les différents types de bijections entre le groupe symétrique et les chemins de Motzkin valués.)

Randrianarivony, Arthur (1995)

Séminaire Lotharingien de Combinatoire [electronic only]

Coxeter-like complexes.

Babson, Eric, Reiner, Victor (2004)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

Cyclic sieving for longest reduced words in the hyperoctahedral group.

Petersen, T.Kyle, Serrano, Luis (2010)

The Electronic Journal of Combinatorics [electronic only]

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