Zeros of Generalized Eulerian Polynomials

Monday, November 10, 2014 - 3:30pm - 3:55pm
Keller 3-180
Mirkó Visontai (Google Inc.)
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.
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