Combinatorial applications of the Hodge-Riemann relations

TL;DR

This paper explores why many natural sequences are log-concave by linking it to standard conjectures, providing explanations and examples from combinatorics.

Contribution

It offers a novel perspective connecting log-concavity in sequences to standard conjectures, with illustrative combinatorial examples.

Findings

Sequences often exhibit log-concavity due to underlying geometric principles.

The paper provides combinatorial examples supporting the theoretical explanation.

Links between standard conjectures and combinatorial sequence properties are established.

Abstract

Why do natural and interesting sequences often turn out to be log-concave? We give one of many possible explanations, from the viewpoint of "standard conjectures". We illustrate with several examples from combinatorics.