Generalized noncrossing partitions and combinatorics of Coxeter groups
نویسندگان
چکیده
منابع مشابه
Clusters, Coxeter-sortable Elements and Noncrossing Partitions
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.
متن کاملNoncrossing Partitions, Clusters and the Coxeter Plane
When W is a finite Coxeter group of classical type (A, B, or D), noncrossing partitions associated to W and compatibility of almost positive roots in the associated root system are known to be modeled by certain planar diagrams. We show how the classical-type constructions of planar diagrams arise uniformly from projections of smallW -orbits to the Coxeter plane. When the construction is applie...
متن کاملClusters, Noncrossing Partitions and the Coxeter Plane Nathan Reading
The present research is a contribution to W -Catalan combinatorics, which concerns generalizations of objects counted by the Catalan number to an arbitrary finite Coxeter group W. Triangulations of a polygon are a special case of the combinatorial clusters appearing in the theory of cluster algebras of finite type. Planar diagrams analogous to triangulations encode the combinatorics of clusters...
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We study oscillations in the eigenfunctions for a fractional Schrödinger operator on the real line. An argument in the spirit of Courant’s nodal domain theorem applies to an associated local problem in the upper half plane and provides a bound on the number of nodal domains for the extensions of the eigenfunctions. Using the combinatorial properties of noncrossing partitions, we turn the nodal ...
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2009
ISSN: 0065-9266,1947-6221
DOI: 10.1090/s0065-9266-09-00565-1