Abstract
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 language | English |
|---|---|
| Pages (from-to) | 113-155 |
| Number of pages | 43 |
| Journal | Journal of Combinatorial Theory - Series A |
| Volume | 113 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2006 |
| Externally published | Yes |
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Keywords
- 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
Cite this
Applications of minor summation formula III, Plücker relations, lattice paths and Pfaffian identities. / Ishikawa, Masao; Wakayama, Masato.
In: Journal of Combinatorial Theory - Series A, Vol. 113, No. 1, 01.2006, p. 113-155.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Applications of minor summation formula III, Plücker relations, lattice paths and Pfaffian identities
AU - Ishikawa, Masao
AU - Wakayama, Masato
PY - 2006/1
Y1 - 2006/1
N2 - 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.
AB - 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.
KW - Cauchy identity
KW - Lattice paths method
KW - Lewis Carroll formula
KW - Minor summation formula
KW - Partition
KW - Pfaffian
KW - Plücker relations
KW - q-series
KW - Schur function
UR - http://www.scopus.com/inward/record.url?scp=30444443612&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=30444443612&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2005.05.008
DO - 10.1016/j.jcta.2005.05.008
M3 - Article
VL - 113
SP - 113
EP - 155
JO - Journal of Combinatorial Theory - Series A
JF - Journal of Combinatorial Theory - Series A
SN - 0097-3165
IS - 1
ER -