Noncrossing partitions, Bruhat order and the cluster complex
نویسندگان
چکیده
منابع مشابه
Noncrossing partitions and the shard intersection order
We define a new lattice structure (W, ) on the elements of a finite Coxeter group W. This lattice, called the shard intersection order, is weaker than the weak order and has the noncrossing partition lattice NC(W ) as a sublattice. The new construction of NC(W ) yields a new proof that NC(W ) is a lattice. The shard intersection order is graded and its rank generating function is the W -Euleria...
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Let Φ be an finite root system with corresponding reflection group W and let m be a nonnegative integer. We consider the generalized cluster complex ∆(Φ) defined by S. Fomin and N. Reading and the poset NC(m)(W ) of m-divisible noncrossing partitions defined by D. Armstrong. We give a characterization of the faces of ∆(Φ) in terms of NC(m)(W ), generalizing that of T. Brady and C. Watt given in...
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Each positive rational number x > 0 can be written uniquely as x = a/(b− a) for coprime positive integers 0 < a < b. We will identify x with the pair (a, b). In this paper we define for each positive rational x > 0 a simplicial complex Ass(x) = Ass(a, b) called the rational associahedron. It is a pure simplicial complex of dimension a − 2, and its maximal faces are counted by the rational Catal...
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ژورنال
عنوان ژورنال: Annales de l'Institut Fourier
سال: 2019
ISSN: 1777-5310
DOI: 10.5802/aif.3294