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Abacus proofs of Schur function identities

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dc.contributorVirginia Techen
dc.contributor.authorLoehr, N. A.en
dc.contributor.departmentMathematicsen
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:03Zen
dc.date.available2014-05-28T18:35:03Zen
dc.date.issued2010en
dc.description.abstractThis article uses combinatorial objects called labeled abaci to give direct combinatorial proofs of many familiar facts about Schur polynomials. We use abaci to prove the Pieri rules, the Littlewood-Richardson rule, the equivalence of the tableau definition and the determinant definition of Schur polynomials, and the combinatorial interpretation of the inverse Kostka matrix (first given by Egecioglu and Remmel). The basic idea is to regard formulas involving Schur polynomials as encoding bead motions on abaci. The proofs of the results just mentioned all turn out to be manifestations of a single underlying theme: when beads bump, objects cancel.en
dc.description.sponsorshipNSA research grant H98230-08-1-0045en
dc.identifier.citationLoehr, N. A., "Abacus proofs of Schur function identities," SIAM J. Discrete Math., 24(4), 1356-1370, (2010). DOI: 10.1137/090753462en
dc.identifier.doihttps://doi.org/10.1137/090753462en
dc.identifier.issn0895-4801en
dc.identifier.urihttp://hdl.handle.net/10919/48140en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/090753462en
dc.language.isoen_USen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectabacien
dc.subjectschur functionsen
dc.subjectpieri rulesen
dc.subjectlittlewood-richardson rulesen
dc.subjectsymmetric polynomialsen
dc.subjecttableauxen
dc.subjectinverse kostka matrixen
dc.subjectmathematics, applieden
dc.titleAbacus proofs of Schur function identitiesen
dc.title.serialSiam Journal on Discrete Mathematicsen
dc.typeArticle - Refereeden

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