Séminaire Lotharingien de Combinatoire, B77i (2018), 64 pp.
Gamma-Positivity in Combinatorics and Geometry
Gamma-positivity is an elementary property that
polynomials with symmetric coefficients may have,
which directly implies their unimodality. The
idea behind it stems from work of Foata,
Schützenberger and Strehl on the Eulerian
polynomials; it was revived independently by
Brändén and Gal in the course of their study
of poset Eulerian polynomials and face
enumeration of flag simplicial spheres, respectively,
and has found numerous applications since then.
This paper surveys some of the main results and
open problems on gamma-positivity, appearing in
various combinatorial or geometric contexts, as
well as some of the diverse methods that have
been used to prove it.
Received: November 20, 2017.
Accepted: October 20, 2018.
Final Version: October 23, 2018.
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