## Abstract

In the open problem session of the FPSAC'03, R.P. Stanley gave an open problem about a certain sum of the Schur functions (See [19]). The purpose of this paper is to give a proof of this open problem. The proof consists of three steps. At the first step we express the sum by a Pfaffian as an application of our minor summation formula ([7]). In the second step we prove a Pfaffian analogue of Cauchy type identity which generalize [22]. Then we give a proof of Stanley's open problem in Section 4. We also present certain corollaries obtained from this identity involving the Big Schur functions and some polynomials arising from the Macdonald polynomials, which generalize Stanley's open problem.

Original language | English |
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Pages | 219-230 |

Number of pages | 12 |

Publication status | Published - Dec 1 2005 |

Externally published | Yes |

Event | 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, Italy Duration: Jun 20 2005 → Jun 25 2005 |

### Other

Other | 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 |
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Country | Italy |

City | Taormina |

Period | 6/20/05 → 6/25/05 |

## ASJC Scopus subject areas

- Algebra and Number Theory