A note on passing from a quasi-symmetric function expansion to a Schur\n function expansion of a symmetric function

2018/02/26 by Adriano M. Garsia, Garsia, Adriano, Jeffrey B. Remmel +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1802.09686

openalex publication_date 2018/02/26 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Egge, Loehr and Warrington gave in citeELW a combinatorial formula that\npermits to convert the expansion of a symmetric function, homogeneous of degree\nn, in terms of Gessel's fundamental quasisymmetric functions into an\nexpansion in terms of Schur functions. Surprisingly the Egge, Loehr and\nWarrington result may be shown to be simply equivalent to replacing the Gessel\nfundamental by a Schur function indexed by the same composition. In this paper\nwe give a direct proof of the validity of this replacement. This interpretation\nof the result in citeELW has already been successfully applied to Schur\npositivity problems.\n

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