SB-Labelings, Distributivity, and Bruhat Order on Sortable Elements
نویسندگان
چکیده
منابع مشابه
SB-Labelings, Distributivity and Bruhat Order on Sortable Elements
In this article, we investigate the set of γ-sortable elements, associated with a Coxeter group W and a Coxeter element γ ∈ W , under Bruhat order, and we denote this poset by Bγ . We show that this poset belongs to the class of SB-lattices recently introduced by Hersh and Mészáros, by proving a more general statement, namely that all join-distributive lattices are SB-lattices. The observation ...
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We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in terms of their inversion sets and, in the classical cases, in terms of permutations.
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A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space HPP generated by PP , using the notion of biideals of plane posets. We here define a partial order on PP , making it isomorphic to the set of partitions with t...
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We show that the principal order ideal of an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motzkin...
متن کاملSortable Elements in Infinite Coxeter Groups
In a series of previous papers, we studied sortable elements in finite Coxeter groups, and the related Cambrian fans. We applied sortable elements and Cambrian fans to the study of cluster algebras of finite type and the noncrossing partitions associated to Artin groups of finite type. In this paper, as the first step towards expanding these applications beyond finite type, we study sortable el...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4942