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Christos Athanasiadis:On the gamma-positivity of the Eulerian transformation

Time: Wed 2022-11-09 10.15 - 11.15

Video link: Meeting ID: 637 4378 6038

Participating: Christos Athanasiadis (University of Athens)

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Abstract: The Eulerian transformation is the linear operator on polynomials in one variable with real coefficients which maps the powers of the variable to the corresponding Eulerian polynomials. Brändén and Jochemko have conjectured that the Eulerian transforms of a class of polynomials with nonnegative coefficients, including those which have only real roots and all lying in the interval [-1,0], are real-rooted and proved that they have nonnegative and unimodal symmetric decompositions. We will establish the stronger property that these transforms have gamma-positive symmetric decompositions and show how to generalize this statement, as well as the conjecture of Brändén and Jochemko, in the context of uniform triangulations of simplicial complexes.