Name: On Newton's identities in positive characteristic
Creator: Sjoerd de Vries
Keywords: Symmetric functions and generalizations, symmetric polynomials, Symmetric polynomials, FOS: Mathematics, Mathematics - Combinatorics, Newton's identities, Combinatorics (math.CO), Representation Theory (math.RT), Algebra and Logic, 05E05 (Primary) 11T06 (Secondary)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Apr 2025Embargo end date: 01 Jan 2023 English Publisher:Elsevier BVJournal:Journal of Algebra, volume 668, pages 348-364 (issn: 0021-8693,

Authors: Sjoerd de Vries;

doi: 10.1016/j.jalgebra.2025.01.010 , 10.48550/arxiv.2305.19850

arXiv: 2305.19850

On Newton's identities in positive characteristic

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Abstract

Newton's identities provide a way to express elementary symmetric polynomials in terms of power polynomials over fields of characteristic zero. In this article, we study the failure of this relation in positive characteristic and what can be recovered. In particular, we show how one can write the elementary symmetric polynomials as rational functions in the power polynomials over any commutative unital ring.

Final version, to appear in J. Alg

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Stockholm University
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Keywords

Symmetric functions and generalizations, symmetric polynomials, Symmetric polynomials, FOS: Mathematics, Mathematics - Combinatorics, Newton's identities, Combinatorics (math.CO), Representation Theory (math.RT), Algebra and Logic, 05E05 (Primary) 11T06 (Secondary), Mathematics - Representation Theory, Algebra och logik

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