Strong Log-Concavity Does Not Imply Log-Submodularity

TL;DR

This paper disproves a conjecture by showing that strong log-concavity of discrete distributions does not necessarily imply log-submodularity, challenging assumptions about their relationship.

Contribution

It provides a counterexample demonstrating that strong log-concavity does not imply log-submodularity in discrete distributions.

Findings

Counterexample disproves the conjecture

Challenges previous assumptions about distribution properties

Clarifies the relationship between log-concavity and log-submodularity

Abstract

We disprove a recent conjecture regarding discrete distributions and their generating polynomials stating that strong log-concavity implies log-submodularity.