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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...

Canonical Brauer induction and symmetric groups

Robert Boltje, Burkhard Külshammer (2005)

Bollettino dell'Unione Matematica Italiana

Imitating the approach of canonical induction formulas we derive a formula that expresses every character of the symmetric group as an integer linear combination of Young characters. It is different from the well-known formula that uses the determinantal form.

Canonical characters on simple graphs

Tanja Stojadinović (2013)

Czechoslovak Mathematical Journal

A multiplicative functional on a graded connected Hopf algebra is called the character. Every character decomposes uniquely as a product of an even character and an odd character. We apply the character theory of combinatorial Hopf algebras to the Hopf algebra of simple graphs. We derive explicit formulas for the canonical characters on simple graphs in terms of coefficients of the chromatic symmetric function of a graph and of canonical characters on quasi-symmetric functions. These formulas and...

Categorification of the virtual braid groups

Anne-Laure Thiel (2011)

Annales mathématiques Blaise Pascal

We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.

Characters of finite quasigroups VII: permutation characters

Kenneth Walter Johnson, Jonathan D. H. Smith (2004)

Commentationes Mathematicae Universitatis Carolinae

Each homogeneous space of a quasigroup affords a representation of the Bose-Mesner algebra of the association scheme given by the action of the multiplication group. The homogeneous space is said to be faithful if the corresponding representation of the Bose-Mesner algebra is faithful. In the group case, this definition agrees with the usual concept of faithfulness for transitive permutation representations. A permutation character is associated with each quasigroup permutation representation,...

Chess tableaux.

Chow, Timothy Y., Eriksson, Henrik, Fan, Kenneth C. (2005)

The Electronic Journal of Combinatorics [electronic only]

Combinatoria e Topologia. Alcune considerazioni generali

Andrea Brini (2003)

Bollettino dell'Unione Matematica Italiana

Si descrive un metodo generale mediante il quale associare in modo naturale spazi topologici ad insiemi parzialmente ordinati e funzioni continue afunzioni monotone tra di essi; questa associazione è chiaramente la chiave di volta per fondare l’utilizzo di metodi topologici nella teoria combinatoria degli insiemi parzialmente ordinati. Si discutono quindi alcuni criteri di contraibilità e si presenta una breve introduzione alla teoria dei «poset Cohen-Macaulay». Il lavoro si conclude con una sezione...

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