### 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(Mat_{q}(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 |
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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

*Linear and Multilinear Algebra*,

*39*(3), 285-305. https://doi.org/10.1080/03081089508818403

**Minor Summation Formula of Pfaffians.** / Ishikawa, Masao; Wakayama, Masato.

Research output: Contribution to journal › Article

*Linear and Multilinear Algebra*, vol. 39, no. 3, pp. 285-305. https://doi.org/10.1080/03081089508818403

}

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 -