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We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. This construction provides polytopal realizations for a certain class of subword complexes containing all cluster complexes of finite types. For the latter, the brick polytopes turn out to coincide with the known realizations of generalized… (More)

We exhibit a canonical connection between maximal (0, 1)-fillings of a moon polyomino avoiding northeast chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable, and thus shellable, sphere. In particular, this implies a positivity… (More)

We study bijections { Set partitions of type X } ˜ −→ { Set partitions of type X } • either the number of crossings and of nestings, • or the cardinalities of a maximal crossing and of a maximal nesting. In type D, the results are obtained only in the case of non-crossing and non-nesting set partitions. In all types, we show in particular that non-crossing… (More)

We describe edge labelings of the increasing flip graph of a sub-word complex on a finite Coxeter group, and study applications thereof. On the one hand, we show that they provide canonical spanning trees of the facet-ridge graph of the subword complex, describe inductively these trees, and present their close relations to greedy facets. Searching these… (More)

We show that the vertex barycenter of generalized associahedra and permutahedra coincide for any finite Coxeter system.

In this paper, we count factorizations of Coxeter elements in well-generated complex reflection groups into products of reflections. We obtain a simple product formula for the exponential generating function of such factor-izations, which is expressed uniformly in terms of natural parameters of the group. In the case of factorizations of minimal length, we… (More)

- Christian Stump
- 2014

In this note, we provide a bijection between a new collection of words on nonnegative integers of length n and Dyck paths of length 2n − 2, thus proving that this collection belongs to the Catalan family. The surprising key step in this bijection is the zeta map which is an important map in the study of q, t-Catalan numbers. Finally we discuss an… (More)

The FindStat project provides an online platform for mathematicians, particularly for combinatorialists, to gather information about combinatorial statistics and their relations. As of January 2014, the FindStat database contains 173 statistics on 17 combinatorial collections. Combinatorial statistics arise naturally all over mathematics. Before we give the… (More)