Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/11472
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Azenhas, Olga | - |
dc.date.accessioned | 2009-09-18T12:31:37Z | - |
dc.date.available | 2009-09-18T12:31:37Z | - |
dc.date.issued | 2000 | - |
dc.identifier.citation | Pré-Publicações DMUC. 00-27 (2000) | en_US |
dc.identifier.uri | https://hdl.handle.net/10316/11472 | - |
dc.description.abstract | The original definition of the Littlewood-Richardson (LR) rule for composing partitions is exclusively considered, i. e., the classical combinatorial device for calculating the Littlewood-Richardson coefficients. The main result is an explicit involution on the set of LR tableaux which transforms an LR tableau of type [a, b, c] into one of type [b, a, c]. On the basis of the involution definition it is a projection of LR tableaux of order r into those of order r - 1, for r ~ 1. The main feature of this projection is the decomposition of an LR tableau of order r and type [a, b, c] into a nested sequence of LR tableaux of order s and type [a(s), (b1, ... , bs); (Cr-s+l, ... , cr )], s == 1, ... , r, where (a(s))~==l is a sequence of interlacing partitions which defines a decomposition of an LR tableau of type [b, a, c] into a nested sequence of LR tableaux of order s and type [(b1, ... ,bs);a(s); (Cr-s+l, ... ,cr )], s == 1, ... ,r. This projection is accomplished introducing a combinatorial deletion and insertion operation on a LR tableau preserving the LR conditions. This involution yields a self-contained and direct combinatorial interpretation of the well-known commutative property of the original LR rule, as well as of the symmetry of the Littlewood-Richardson coefficients given by the equality Ngb == N ba . It is known that the LR rule describes the Smith invariants of a product of integral matrices. It has been proven that this rule is also describing the eigenvalues of a sum of Hermitian matrices [13, 14, 17]. With the present involution we aim to a deeper understanding of the structure the LR rule and its relationship with these two problems in matrix theory. | en_US |
dc.description.sponsorship | FCT; CMUC/FCT, project Praxis 2/2.1/MAT/458/94; Fundação LusoAmericana para o Desenvolvimento, project 574/94. | 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 | Young tableaux | en_US |
dc.subject | Littlewood-Richardson rule | en_US |
dc.subject | Projection | en_US |
dc.subject | Involution | en_US |
dc.title | On an involution on the set of Littlewood-Richardson tableaux and the hidden commutativity | en_US |
dc.type | preprint | en_US |
uc.controloAutoridade | Sim | - |
item.fulltext | Com Texto completo | - |
item.openairecristype | http://purl.org/coar/resource_type/c_816b | - |
item.grantfulltext | open | - |
item.languageiso639-1 | en | - |
item.openairetype | preprint | - |
item.cerifentitytype | Publications | - |
crisitem.author.dept | Faculty of Sciences and Technology | - |
crisitem.author.parentdept | University of Coimbra | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0001-7718-7158 | - |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Nacionais |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
On an involution on the set of Littlewood-Richardson tableaux and the hidden commutativity.pdf | 537.2 kB | Adobe PDF | View/Open |
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.