A proof of Stanley's open problem

Research output: Contribution to conferencePaperpeer-review

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 languageEnglish
Pages219-230
Number of pages12
Publication statusPublished - Dec 1 2005
Externally publishedYes
Event17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, Italy
Duration: Jun 20 2005Jun 25 2005

Other

Other17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05
CountryItaly
CityTaormina
Period6/20/056/25/05

ASJC Scopus subject areas

  • Algebra and Number Theory

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