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Explicit computations with the divided symmetrization operator

Author: Tewodros Amdeberhan
Journal: Proc. Amer. Math. Soc. 144 (2016), 2799-2810
MSC (2010): Primary 05E10
Published electronically: October 22, 2015
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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 [Enhancements On Off] (What's this?)

  • [1] 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
  • [2] Alexander Postnikov, Permutohedra, associahedra, and beyond, Int. Math. Res. Not. IMRN 6 (2009), 1026–1106. MR 2487491, 10.1093/imrn/rnn153

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Additional Information

Tewodros Amdeberhan
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118

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
Article copyright: © Copyright 2015 American Mathematical Society