## squarefree monomial ideals and simplicial complexes

Let $I = (f_1, f_2); J = (g_1, g_2), L= (h_1, h_2)$ be monomial ideals in polynomial ring $S = \mathbb{K}[x_1,...,x_n]$ such that $f_1, f_2, g_1, g_2, h_1, h_2 \in S, f_1$ and $f_2$, $g_1$ and $g_2$, $h_1$ and $h_2$ don't contain the same variables.

Find out the relationship between simplicial complex of $I, J, L$ and simplicial complex of the product $IJL$

i thinhk we need to find the polarization of $IJL$. Help me show this, please!

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If you do your homework by yourself you'll learn a lot more. – Angelo Jan 22 at 4:52