Journal
JOURNAL OF COMBINATORIAL THEORY SERIES A
Volume 113, Issue 1, Pages 113-155Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcta.2005.05.008
Keywords
Pfaffian; Plucker relations; Lewis Carroll formula; partition; lattice paths method; minor summation; formula; Cauchy identity; Schur function; q-series
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The initial purpose of the present paper is to provide a combinatorial proof of the minor summation formula of Pfaffians in [Ishikawa, Wakayama, Minor summation formula of Pfafflans, Linear and Multilinear Algebra 39 (1995) 285-305] based on the lattice path method. The second aim is to study applications of the minor summation formula for obtaining several identities. Especially, a simple proof of Kawanaka's formula concerning a q-series identity involving the Schur functions [Kawanaka, A q-series identity involving Schur functions and related topics, Osaka J. Math. 36 (1999) 157-176] and of the identity in [Kawanaka, A q-Cauchy identity involving Schur functions and imprimitive complex reflection groups, Osaka J. Math. 38 (2001) 775-810] which is regarded as a determinant version of the previous one are given. (c) 2005 Elsevier Inc. All rights reserved.
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