Abstract
In this paper we establish a formula involving Pfaffıans for a certain weighted sum of minors of an arbitrary given matrix. First we find a formula where the sum ranges for all columns, and secondly we obtain a formula where the sum ranges for both all rows and columns as the application of the first one. The first formula is stated in the framework of quantum matrix algebra A(Matq(m, n)). These sums are weighted by “sub-Pfaffıans” of any given (q-)skew symmetric matrices. In the last section we provide an application of the minor summation formula to the generating functions of shifted tableaux.
| Original language | English |
|---|---|
| Pages (from-to) | 285-305 |
| Number of pages | 21 |
| Journal | Linear and Multilinear Algebra |
| Volume | 39 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Aug 1 1995 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Minor Summation Formula of Pfaffians. / Ishikawa, Masao; Wakayama, Masato.
In: Linear and Multilinear Algebra, Vol. 39, No. 3, 01.08.1995, p. 285-305.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Minor Summation Formula of Pfaffians
AU - Ishikawa, Masao
AU - Wakayama, Masato
PY - 1995/8/1
Y1 - 1995/8/1
N2 - In this paper we establish a formula involving Pfaffıans for a certain weighted sum of minors of an arbitrary given matrix. First we find a formula where the sum ranges for all columns, and secondly we obtain a formula where the sum ranges for both all rows and columns as the application of the first one. The first formula is stated in the framework of quantum matrix algebra A(Matq(m, n)). These sums are weighted by “sub-Pfaffıans” of any given (q-)skew symmetric matrices. In the last section we provide an application of the minor summation formula to the generating functions of shifted tableaux.
AB - In this paper we establish a formula involving Pfaffıans for a certain weighted sum of minors of an arbitrary given matrix. First we find a formula where the sum ranges for all columns, and secondly we obtain a formula where the sum ranges for both all rows and columns as the application of the first one. The first formula is stated in the framework of quantum matrix algebra A(Matq(m, n)). These sums are weighted by “sub-Pfaffıans” of any given (q-)skew symmetric matrices. In the last section we provide an application of the minor summation formula to the generating functions of shifted tableaux.
UR - http://www.scopus.com/inward/record.url?scp=84949693968&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84949693968&partnerID=8YFLogxK
U2 - 10.1080/03081089508818403
DO - 10.1080/03081089508818403
M3 - Article
VL - 39
SP - 285
EP - 305
JO - Linear and Multilinear Algebra
JF - Linear and Multilinear Algebra
SN - 0308-1087
IS - 3
ER -