Pruning Processes and a New Characterization of Convex Geometries

TL;DR

This paper introduces a novel characterization of convex geometries using a multivariate identity, linking combinatorial structures in convex geometry with removal processes studied in random structures.

Contribution

It provides a new perspective on convex geometries by connecting them to multivariate identities and removal processes, expanding the understanding of their structural properties.

Findings

New characterization of convex geometries via multivariate identities

Connection established between convex geometries and removal processes

Highlights relationships among different convex geometry characterizations

Abstract

We provide a new characterization of convex geometries via a multivariate version of an identity that was originally proved by Maneva, Mossel and Wainwright for certain combinatorial objects arising in the context of the k-SAT problem. We thus highlight the connection between various characterizations of convex geometries and a family of removal processes studied in the literature on random structures.