Minor summation formula and a proof of Stanley's open problem

研究成果査読

2 被引用数 (Scopus)

抄録

In the open problem session of the FPSAC'03, R.P. Stanley gave an open problem about a certain sum of the Schur functions. 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 (Ishikawa and Wakayama in Linear Multilinear Algebra 39:285-305, 1995). In the second step we prove a Pfaffian analogue of a Cauchy type identity which generalizes Sundquist's Pfaffian identities (J. Algebr. Comb. 5:135-148, 1996). Then we give a proof of Stanley's open problem in Sect. 4. At the end of this paper we 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.

本文言語English
ページ(範囲)211-234
ページ数24
ジャーナルRamanujan Journal
16
2
DOI
出版ステータスPublished - 7月 2008
外部発表はい

ASJC Scopus subject areas

  • 代数と数論

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