Eulerian polynomials of type $D$ have only real rootsReport as inadecuate




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1 NCSU - Department of Mathematics Raleigh 2 Department of Mathematics Stockholm University

Abstract : 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.

Résumé : 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.

Keywords : polynomials with only real roots. inversion sequences Coxeter group of type D Eulerian polynomials





Author: Carla D. Savage - Mirkó Visontai -

Source: https://hal.archives-ouvertes.fr/



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