Please use this identifier to cite or link to this item: https://hdl.handle.net/10316/11472
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dc.contributor.authorAzenhas, Olga-
dc.date.accessioned2009-09-18T12:31:37Z-
dc.date.available2009-09-18T12:31:37Z-
dc.date.issued2000-
dc.identifier.citationPré-Publicações DMUC. 00-27 (2000)en_US
dc.identifier.urihttps://hdl.handle.net/10316/11472-
dc.description.abstractThe 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.sponsorshipFCT; CMUC/FCT, project Praxis 2/2.1/MAT/458/94; Fundação LusoAmericana para o Desenvolvimento, project 574/94.en_US
dc.language.isoengen_US
dc.publisherCentro de Matemática da Universidade de Coimbraen_US
dc.rightsopenAccessen_US
dc.subjectYoung tableauxen_US
dc.subjectLittlewood-Richardson ruleen_US
dc.subjectProjectionen_US
dc.subjectInvolutionen_US
dc.titleOn an involution on the set of Littlewood-Richardson tableaux and the hidden commutativityen_US
dc.typepreprinten_US
uc.controloAutoridadeSim-
item.fulltextCom Texto completo-
item.openairecristypehttp://purl.org/coar/resource_type/c_816b-
item.grantfulltextopen-
item.languageiso639-1en-
item.openairetypepreprint-
item.cerifentitytypePublications-
crisitem.author.deptFaculty of Sciences and Technology-
crisitem.author.parentdeptUniversity of Coimbra-
crisitem.author.researchunitCMUC - Centre for Mathematics of the University of Coimbra-
crisitem.author.orcid0000-0001-7718-7158-
Appears in Collections:FCTUC Matemática - Artigos em Revistas Nacionais
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