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

2004/08/16 by Masao Ishikawa, Ishikawa, Masao · 1 citation
Mathematics · #05E05 #05E10 #05E19 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0408204

openalex publication_date 2004/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the open problem session of the FPSAC'03, R.P.Stanley gave an open problem. The purpose of this paper is to give a proof of this open problem. At the end of this paper we present certain corollaries involving the Big Schur functions and some polynomials arising from the Macdonald polynomials, which generalize Stanley's open problem.

Cited by

• On refined enumerations of totally symmetric self-complementary plane partitions I

Related

• A₂ Macdonald polynomials: a separation of variables
• A Generalization of Tokuyama's Formula to the Hall-Littlewood Polynomials
• Elementary Proof of MacMahon's Conjecture
• A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture
• The Stanley Conjecture Revisited