Triangulations of polygons and stacked simplicial complexes: separating their Stanley-Reisner ideals

TL;DR

This paper provides a comprehensive algebraic and combinatorial analysis of Stanley-Reisner ideals associated with polygon triangulations and stacked simplicial complexes, including their separated models.

Contribution

It introduces a complete algebraic and combinatorial framework for understanding Stanley-Reisner ideals of these complexes, extending to stacked polytopes.

Findings

Full characterization of Stanley-Reisner ideals for polygon triangulations

Description of separated models for these ideals

Extension to stacked simplicial complexes and polytopes

Abstract

A triangulation of a polygon has an associated Stanley-Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals, and describe their separated models. More generally we do this for stacked simplicial complexes, in particular for stacked polytopes.