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

Masao Ishikawa, Masato Wakayama

Research output: Contribution to journalArticle

19 Citations (Scopus)


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 Pfaffians, 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.

Original languageEnglish
Pages (from-to)113-155
Number of pages43
JournalJournal of Combinatorial Theory - Series A
Issue number1
Publication statusPublished - Jan 2006
Externally publishedYes



  • Cauchy identity
  • Lattice paths method
  • Lewis Carroll formula
  • Minor summation formula
  • Partition
  • Pfaffian
  • Plücker relations
  • q-series
  • Schur function

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

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