Applications of minor summation formula III, Pluicker relations, lattice paths and Pfaffian identities

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:113

Article

Ishikawa, M ; Wakayama, M

关键词: Pfaffian;    Plucker relations;    Lewis Carroll formula;    partition;    lattice paths method;    minor summation;    formula;    Cauchy identity;    Schur function;    q-series;   

DOI  :  10.1016/j.jcta.2005.05.008

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free