4 papers
Cluster parking functions II: -dihedral sieving via diagonal coinvariants
Matthieu Josuat-Vergès
In a previous work, we defined the complex of cluster parking functions. On one side, they encode the type-refined enumeration of faces of the cluster complex, and on the other sid…
Homology character of the parabolic coset poset
Theo Douvropoulos, Matthieu Josuat-Vergès
Motivated by the analogy with the Coxeter complex on one side, and parking functions on the other side, we study the poset of parabolic cosets in a finite Coxeter group. We show th…
Cluster parking functions
Theo Douvropoulos, Matthieu Josuat-Vergès
The cluster complex on one hand, parking functions on the other hand, are two combinatorial (po)sets that can be associated to a finite real reflection group. Cluster parking funct…
Automorphisms of the generalized cluster complex
Matthieu Josuat-Vergès
It is proved that the generalized cluster complex defined by Fomin and Reading has a dihedral symmetry. Together with diagram symmetries, they generate its automorphism group. A co…