Explicit computations with the divided symmetrization operator
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- by Tewodros Amdeberhan PDF
- Proc. Amer. Math. Soc. 144 (2016), 2799-2810 Request permission
Abstract:
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 and some rational functions. We hope the results to be valuable and available to research practitioners in these areas. In addition, the methods of proof utilized here are simple and amenable to many more analogous computations.References
- Alain Lascoux, Symmetric functions and combinatorial operators on polynomials, CBMS Regional Conference Series in Mathematics, vol. 99, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2003. MR 2017492, DOI 10.1090/cbms/099
- Alexander Postnikov, Permutohedra, associahedra, and beyond, Int. Math. Res. Not. IMRN 6 (2009), 1026–1106. MR 2487491, DOI 10.1093/imrn/rnn153
Additional Information
- Tewodros Amdeberhan
- Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
- MR Author ID: 260444
- Email: tamdeber@tulane.edu
- Received by editor(s): July 9, 2015
- Received by editor(s) in revised form: August 23, 2015
- Published electronically: October 22, 2015
- Communicated by: Ken Ono
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2799-2810
- MSC (2010): Primary 05E10
- DOI: https://doi.org/10.1090/proc/12931
- MathSciNet review: 3487215