Gunnar Fløystad: Separating and joining variables in monomial ideals

Abstract

This is a simple technique but with natural applications and leading to heightened structural understanding. 

We get a full algebraic and combinatorial understanding of Stanley-Reisner ideals of triangulations of polygons and more generally of stacked simplicial complexes. We conjecture that all separations of artinian monomial ideals to squarefree monomial ideals correspond to triangulations of balls, and give a number of examples.