منابع مشابه
Coxeter-Catalan Combinatorics
In this talk we will introduce the new and active topic “CoxeterCatalan combinatorics”. We will survey three trends, namely the nonnesting partitions, noncrossing partitions and cluster complexes, leading to this topic. Some new results and unsolved problems will be given.
متن کاملGeneralized Cluster Complexes and Coxeter Combinatorics
In the first part of this paper (Sections 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12), we introduce and study a simplicial complex ∆(Φ) associated to a finite root system Φ and a nonnegative integer parameter m. For m = 1, our construction specializes to the (simplicial) generalized associahedra ∆(Φ) introduced in [13] and identified in [14] as the underlying complexes for the cluster algebras of f...
متن کاملThe type A Coxeter complex in algebraic combinatorics
Coxeter complexes are simplicial polytopes derived from certain reflection groups. The type An−1 Coxeter complex is derived from the symmetric group Sn and admits an elegant combinatorial description. Its faces are identified with set compositions and certain combinatorial properties of these compositions can be explained geometrically. Aguiar and Mahajan used this geometry to define a product ...
متن کاملCombinatorics of sections of polytopes and Coxeter groups in Lobachevsky spaces
Coxeter classified all discrete isometry groups generated by reflections that act on a Euclidean space or on a sphere of an arbitrary dimension (see [1]). His fundamental work became classical long ago. Lobachevsky spaces (classical hyperbolic spaces) are as symmetric as Euclidean spaces and spheres. However, discrete isometry groups generated by reflections, with fundamental polytopes of finit...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2017
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-017-0775-1