Noncrossing partitions and Bruhat order
| Autor: | Thomas Gobet, Nathan Williams |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Monoid
Mathematics::Combinatorics Noncrossing partition 010102 general mathematics Coxeter group Distributive lattice Group Theory (math.GR) 0102 computer and information sciences Basis (universal algebra) 01 natural sciences Bruhat order Combinatorics Mathematics::Group Theory 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) 0101 mathematics Mathematics::Representation Theory Partially ordered set Mathematics - Group Theory Coxeter element Mathematics |
| Zdroj: | European Journal of Combinatorics. 53:8-34 |
| ISSN: | 0195-6698 |
| DOI: | 10.1016/j.ejc.2015.10.007 |
| Popis: | We prove that the restriction of Bruhat order to type A noncrossing partitions for the Coxeter element c = s 1 s 2 ? s n defines a distributive lattice isomorphic to the order ideals of the root poset ordered by inclusion. Motivated by the base change from the graphical basis of the Temperley-Lieb algebra to the image of the simple elements of the dual braid monoid, we extend this bijection to other Coxeter elements using certain canonical factorizations. In particular, we introduce a new set of vectors counted by the Catalan numbers and give new bijections-fixing each reflection-between noncrossing partitions associated to distinct Coxeter elements. |
| Databáze: | OpenAIRE |
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