Explicit computations with the divided symmetrization operator | Zendy

Tewodros Amdeberhan | Zendy

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Explicit computations with the divided symmetrization operator

Author(s) -

Tewodros Amdeberhan

Publication year - 2015

Publication title -

proceedings of the american mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.968

H-Index - 84

eISSN - 1088-6826

pISSN - 0002-9939

DOI - 10.1090/proc/12931

Subject(s) - symmetrization , mathematics , computation , polynomial , operator (biology) , simple (philosophy) , rational function , variety (cybernetics) , function (biology) , pure mathematics , algebra over a field , algorithm , combinatorics , mathematical analysis , statistics , biochemistry , chemistry , philosophy , epistemology , repressor , evolutionary biology , biology , transcription factor , gene

Given a multi-variable polynomial, there is an associated divided symmetrization (in particular turning it into a symmetric function). Postinkov has found the volume of a permutohedron as a divided symmetrization (DS) of the power of a certain linear form. The main task in this paper is to exhibit and prove closed form DS-formulas for a variety of polynomials. We hope the results to be valuable and available to the research practitioner in these areas. Also, the methods of proof utilized here are simple and amenable to many more analogous computations. We conclude the paper with a list of such formulas.

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