Utilize este identificador para referenciar este registo:
https://hdl.handle.net/10316/13627
Título: | On an index two subgroup of puzzle and Littlewood-Richardson tableau Z2 x S3-symmetries | Autor: | Azenhas, Olga Conflitti, Alessandro Mamede, Ricardo |
Palavras-chave: | Litlewood-Richardson coefficients; Mosaics; Puzzles; Tableaux; Action of the dihedral group of cardinality twelve | Data: | 2009 | Editora: | Centro de Matemática da Universidade de Coimbra | Citação: | Pré-Publicações DMUC. 09-51 (2009) | Título da revista, periódico, livro ou evento: | Pré-Publicações DMUC | Número: | 09-51 | Resumo: | We consider an action of the dihedral group Z2 × S3 on Littlewood- Richardson tableaux which carries a linear time action of a subgroup of index two. This index two subgroup action on Knutson-Tao-Woodward puzzles is the group generated by the puzzle mirror reflections with label swapping. One shows that, as happens in puzzles, half of the twelve symmetries of Littlewood-Richardson coefficients may also be exhibited on Littlewood-Richardson tableaux by surprisingly easy maps. The other hidden half symmetries are given by a remaining generator which enables to reduce those symmetries to the Sch¨utzenberger involution. Purbhoo mosaics are used to map the action of the subgroup of index two on Littlewood- Richardson tableaux into the group generated by the puzzle mirror reflections with label swapping. After Pak and Vallejo one knows that Berenstein-Zelevinsky triangles, Knutson-Tao hives and Littlewood-Richardson tableaux may be put in correspondence by linear algebraic maps. We conclude that, regarding the symmetries, the behaviour of the various combinatorial models for Littlewood-Richardson coefficients is similar, and the bijections exhibiting them are in a certain sense unique. | URI: | https://hdl.handle.net/10316/13627 | Direitos: | openAccess |
Aparece nas coleções: | FCTUC Matemática - Vários |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
---|---|---|---|---|
On an index two subgroup of puzzle.pdf | 221.07 kB | Adobe PDF | Ver/Abrir |
Visualizações de página
264
Visto em 24/set/2024
Downloads
74
Visto em 24/set/2024
Google ScholarTM
Verificar
Todos os registos no repositório estão protegidos por leis de copyright, com todos os direitos reservados.