Carla D. Savage ; Mirkó Visontai - Eulerian polynomials of type $D$ have only real roots

dmtcs:2321 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2321
Eulerian polynomials of type $D$ have only real rootsConference paper

Authors: Carla D. Savage 1; Mirkó Visontai 2,3

  • 1 Department of Mathematics [Raleigh]
  • 2 Department of Mathematics Stockholm University
  • 3 Department of Mathematics [Stockholm]

[en]
We give an intrinsic proof of a conjecture of Brenti that all the roots of the Eulerian polynomial of type $D$ are real and a proof of a conjecture of Dilks, Petersen, and Stembridge that all the roots of the affine Eulerian polynomial of type $B$ are real, as well.

[fr]
Nous prouvons, de façon intrinsèque, une conjecture de Brenti affirmant que toutes les racines du polynôme eulérien de type $D$ sont réelles. Nous prouvons également une conjecture de Dilks, Petersen, et Stembridge que toutes les racines du polynôme eulérien affine de type $B$ sont réelles.

https://doi.org/10.46298/dmtcs.2321
Source: HAL:hal-01229739v1
Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] Eulerian polynomials, Coxeter group of type D, inversion sequences, polynomials with only real roots.
Funding:
    Source : OpenAIRE Graph
  • Triangle Lectures in Combinatorics; Funder: National Science Foundation; Code: 1202691

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