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dc.contributor.authorAzenhas, Olga-
dc.contributor.authorConflitti, Alessandro-
dc.contributor.authorMamede, Ricardo-
dc.identifier.citationPré-Publicações DMUC. 08-56 (2008)en_US
dc.description.abstractBenkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the conjugation symmetry of the Littlewood–Richardson coefficients, i.e. c μ, = c t μt, t . Tableau–switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon–Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Sch¨utzenberger involution and reciprocally. Thus the Benkart–Sottile–Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Sch¨utzenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo.en_US
dc.description.sponsorshipCentro de Matemática da Universidade Coimbra ; FCT Portuguese Foundation of Science and Technology Grant SFRH/BPD/30471/2006.en_US
dc.publisherCentro de Matemática da Universidade de Coimbraen_US
dc.subjectSymmetry maps of Littlewood–Richardson coefficientsen_US
dc.subjectConjugation symmetry mapen_US
dc.subjectLinearly time reduction of Young tableaux bijectionsen_US
dc.subjectTableau– switchingen_US
dc.subjectSchützenberger involutionen_US
dc.titleLinear time equivalence of Littlewood-Richardson coefficient symmetry mapsen_US
item.fulltextCom Texto completo-
item.languageiso639-1en- of Sciences and Technology- of Sciences and Technology- of Coimbra- of Coimbra- - Centre for Mathematics of the University of Coimbra- - Centre for Mathematics of the University of Coimbra-
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