Christophe Hohlweg

Realizations of the Associahedron and Cyclohedron

We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them with the permutahedron of type A and B, respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type An or Bn as the only input data and which specializes to a procedure presented by J.-L. Loday for a certain orientation of An. The described realizations have cambrian fans of type A and B as normal fans. This settles a conjecture of N. Reading for cambrian lattices of these types.

A Solomon descent theory for the wreath products ≀_{}

We propose an analogue of Solomons descent theory for the case of a wreath product G/G n , where G is a finite abelian group. Our construction mixes a number of ingredients: Mantaci-Reutenauer algebras, Spechts theory for the representations of wreath products, Okadas extension to wreath products of the Robinson-Schensted correspondence, and Poiriers quasisymmetric functions. We insist on the functorial aspect of our definitions and explain the relation of our results with previous work concerning the hyperoctaedral group.

Coloured peak algebras and Hopf algebras

For G a finite abelian group, we study the properties of general equivalence relations on Gn = Gn⋊

On inversion sets and the weak order in Coxeter groups

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Minimal and maximal elements in two-sided cells of Sn and Robinson-Schensted correspondence

n, the wreath product of G with the symmetric group

Permutahedra and generalized associahedra

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