Applications of Minor Summation Formula III, Plucker Relations, Lattice Paths and Pfaffian Identities

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dc.creatorIshikawa, Masao
dc.creatorWakayama, Masato
dc.date2003-12-18
dc.date2005-06-05
dc.date.accessioned2026-07-07T06:25:32Z
dc.date.available2026-07-07T06:25:32Z
dc.descriptionThe initial purpose of this paper is to provide a combinatorial proof of the minor summation formula of Pfaffians based on the lattice path method. There we related Plücker relations with the minor summation formula of Pfaffians to simplify its proof by lattice paths. The second aim is to find a various applications of the minor summation formula. First we studied a variant of the Sundquist formula established in J. Alg. Combin. {\bf 5} (1996). Next we gave a simple proof of Kawanaka's formula concerning a $q$-series identity involving Schur functions in Osaka J. Math. {\bf 36} (1999). We also establish a certain identity similar to the Kawanaka formula, and give a combinatorial proof of the determinant version of his formula in Osaka J. Math. {\bf 38} (2001).
dc.description39 pages, LaTeX; typos corrected
dc.identifierhttps://arxiv.org/abs/math/0312358
dc.identifierhttp://arxiv.org/abs/math/0312358
dc.identifierJ. Combin. Theory Ser. A. 113, (2006) 113-155
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96852
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject05E05 (Primary); 05E10, 05A30 (Secondly)
dc.titleApplications of Minor Summation Formula III, Plucker Relations, Lattice Paths and Pfaffian Identities
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