Section: New Results
A note on gamma triangles and local gamma vectors
Alin Bostan contributed to F. Chapoton's article [5] by writing an appendix, which allowed the author to complete its article. The theme of [5] is the study of simplicial complexes in algebraic combinatorics. A basic invariant is the -vector that counts faces according to their dimensions. A less understood invariant is the -vector, introduced by Gal in 2005. Also in 2005, Chapoton, motivated by the study of the combinatorics of simplicial complexes attached to cluster algebras, considered a refined version of the -vector. The main aim of [5] is to introduce the analogue in this context of the -vector, and a further refinement called the -triangle. The author computed explicitly the -triangle for all the cluster simplicial complexes of irreducible Coxeter groups. Alin Bostan contributed to the proof of an unexpected relation between the -triangles of cluster fans of type and .