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Zeros of Generalized Eulerian Polynomials

Presenter
November 10, 2014
Keywords:
  • Eulerian
MSC:
  • 05C45
Abstract
In joint work with Carla Savage, we studied the inversion sequence representation of Eulerian polynomials and their generalizations. This led us to new recurrences for the generalized Eulerian polynomials and their refinements. These recurrences, combined with a relaxed notion of interlacing polynomials, called compatible polynomials, can be used to prove that all zeros of the generalized Eulerian polynomials are real. A slight modification of this method settles a conjecture of Brenti from 1994 in the affirmative.