Mathematics – Combinatorics
Scientific paper
2005-05-05
Int. Math. Res. Notices 2005, no. 44, 2709-2757
Mathematics
Combinatorics
The only change in this version is that the introduction was made into a numbered section. This was done to make the arXiv ver
Scientific paper
We introduce and study a family of simplicial complexes associated to an arbitrary finite root system and a nonnegative integer parameter m. For m=1, our construction specializes to the (simplicial) generalized associahedra or, equivalently, to the cluster complexes for the cluster algebras of finite type. Our computation of the face numbers and h-vectors of these complexes produces the enumerative invariants defined in other contexts by C.A.Athanasiadis, suggesting links to a host of well studied problems in algebraic combinatorics of finite Coxeter groups, root systems, and hyperplane arrangements. Recurrences satisfied by the face numbers of our complexes lead to combinatorial algorithms for determining Coxeter-theoretic invariants. That is, starting with a Coxeter diagram of a finite Coxeter group, one can compute the Coxeter number, the exponents, and other classical invariants by a recursive procedure that only uses most basic graph-theoretic concepts applied to the input diagram. In types A and B, we rediscover the constructions and results obtained by E.Tzanaki
Fomin Sergey
Reading Nathan
No associations
LandOfFree
Generalized cluster complexes and Coxeter combinatorics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized cluster complexes and Coxeter combinatorics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized cluster complexes and Coxeter combinatorics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-114169