Gamma-positivity in combinatorics and geometry

By Christos A. Athanasiadis. 2017

160 citations recorded by the source corpus.

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, Sch\"utzenberger and Strehl on the Eulerian polynomials; it was revived independently by Br\"and\'en 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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/174f2388f1cda17edc702c5f418b3f4d306d2ecc

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In Algebra and Number Theory

1. Liam Solus
2. Petter Brand'en

In Discrete Mathematics and Combinatorics

1. Liam Solus
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In Geometry and Topology

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Citations in the corpus

• Symmetric Decompositions and Real-Rootedness (2018, background): “This polynomial, as well as the polynomial a in (a, b), was conjectured by Athanasiadis to be real-rooted [2, Question 4.11], [3, Conjecture 2.30], [29, Conjecture 3.7.10].”