Simplicial Complexes have Stanley Reisner Ideals in Abstract Algebra. From what I understand, the ideal is generated by listing the minimal missing edges, faces, facets etc. I've drawn a few examples below and would like to see if the simplicial complex I've drawn matches the associated Stanley Reisner ideal.
Further, I know that these ideals are supposed to be monomials with positive exponents. As you can see, I can't really see how an exponent would be used in this setting. ie - in what instance would I write $w^2$ or $(uv)^3$?