### Abstract

The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.

Original language | English |
---|---|

Pages (from-to) | 136-157 |

Number of pages | 22 |

Journal | Journal of Combinatorial Theory - Series A |

Volume | 88 |

Issue number | 1 |

Publication status | Published - Oct 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Character
- Generating function
- Partition
- Pfaffian
- Schur polynomial

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory - Series A*,

*88*(1), 136-157.

**Applications of Minor-Summation Formula II. Pfaffians and Schur Polynomials.** / Ishikawa, Masao; Wakayama, Masato.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory - Series A*, vol. 88, no. 1, pp. 136-157.

}

TY - JOUR

T1 - Applications of Minor-Summation Formula II. Pfaffians and Schur Polynomials

AU - Ishikawa, Masao

AU - Wakayama, Masato

PY - 1999/10

Y1 - 1999/10

N2 - The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.

AB - The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.

KW - Character

KW - Generating function

KW - Partition

KW - Pfaffian

KW - Schur polynomial

UR - http://www.scopus.com/inward/record.url?scp=0000824310&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000824310&partnerID=8YFLogxK

M3 - Article

VL - 88

SP - 136

EP - 157

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 1

ER -