Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/13627
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Azenhas, Olga | - |
dc.contributor.author | Conflitti, Alessandro | - |
dc.contributor.author | Mamede, Ricardo | - |
dc.date.accessioned | 2010-08-19T13:21:20Z | - |
dc.date.available | 2010-08-19T13:21:20Z | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | Pré-Publicações DMUC. 09-51 (2009) | en_US |
dc.identifier.uri | https://hdl.handle.net/10316/13627 | - |
dc.description.abstract | 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. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Centro de Matemática da Universidade de Coimbra | en_US |
dc.rights | openAccess | en_US |
dc.subject | Litlewood-Richardson coefficients | en_US |
dc.subject | Mosaics | en_US |
dc.subject | Puzzles | en_US |
dc.subject | Tableaux | en_US |
dc.subject | Action of the dihedral group of cardinality twelve | en_US |
dc.title | On an index two subgroup of puzzle and Littlewood-Richardson tableau Z2 x S3-symmetries | en_US |
dc.type | preprint | en_US |
degois.publication.issue | 09-51 | en_US |
degois.publication.title | Pré-Publicações DMUC | en_US |
uc.controloAutoridade | Sim | - |
item.languageiso639-1 | en | - |
item.openairecristype | http://purl.org/coar/resource_type/c_816b | - |
item.grantfulltext | open | - |
item.fulltext | Com Texto completo | - |
item.cerifentitytype | Publications | - |
item.openairetype | preprint | - |
crisitem.author.dept | Faculty of Sciences and Technology | - |
crisitem.author.dept | Faculty of Sciences and Technology | - |
crisitem.author.parentdept | University of Coimbra | - |
crisitem.author.parentdept | University of Coimbra | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0001-7718-7158 | - |
crisitem.author.orcid | 0000-0002-3470-5178 | - |
Appears in Collections: | FCTUC Matemática - Vários |
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File | Description | Size | Format | |
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On an index two subgroup of puzzle.pdf | 221.07 kB | Adobe PDF | View/Open |
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