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https://hdl.handle.net/10316/101354
Título: | Commutation Classes of the Reduced Words for the Longest Element of ${\mathfrak S}_n$ | Autor: | Gutierres, Gonçalo Mamede, Ricardo Nuno Santos, José Luis |
Data: | 2020 | Título da revista, periódico, livro ou evento: | Electronic Journal of Combinatorics | Volume: | 27 | Número: | 2 | Resumo: | Using the standard Coxeter presentation for the symmetric group Sn, two re- duced expressions for the same group element w are said to be commutationally equivalent if one expression can be obtained from the other one by applying a nite sequence of commutations. The commutation classes can be seen as the vertices of a graph bG (w), where two classes are connected by an edge if elements of those classes di er by a long braid relation. We compute the radius and diameter of the graph bG (w0), for the longest element w0 in the symmetric group Sn, and show that it is not a planar graph for n > 6. We also describe a family of commutation classes which contains all atoms, that is classes with one single element, and a subfamily of commutation classes whose elements are in bijection with standard Young tableaux of certain moon-polyomino shapes. | URI: | https://hdl.handle.net/10316/101354 | ISSN: | 1077-8926 | DOI: | 10.37236/9481 | Direitos: | openAccess |
Aparece nas coleções: | I&D CMUC - Artigos em Revistas Internacionais |
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Ficheiro | Descrição | Tamanho | Formato | |
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Commutation-classes-of-the-reduced-words-for-the-longest-element-of-SsubnsubElectronic-Journal-of-Combinatorics.pdf | 413.43 kB | Adobe PDF | Ver/Abrir |
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