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Suppose I have two simplicial complexies $\triangle_1$ and $\triangle_2$. Consider their Stanley-Reisner ideals $I(\triangle_1)$ and $I(\triangle_2)$. I want to get their intersections when they meet at one point and at two points.

How can I express the two different intersections in terms of ideal operations?

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  • $\begingroup$ Could you make your question more precise? Presumably $\Delta_1$ and $\Delta_2$ are simplicial complexes on the same vertex set, and you are interested in the cases where their intersection is a single vertex, or a pair of vertices. Is that correct? $\endgroup$
    – Mark Grant
    Commented May 8, 2017 at 15:46
  • $\begingroup$ @Mark Grant yes you understood correctly. $\endgroup$
    – hhh
    Commented May 8, 2017 at 16:23

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