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Let $ I = (f_1, f_2); J = (g_1, g_2), L= (h_1, h_2) $ be monomial ideals in polynomial ring $ S = 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$.

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i thinhk we need to find the polarization of $IJL$. Help me show this, please! –  daisy Jan 22 '13 at 2:17
Posted also here. –  user26857 Jan 23 '13 at 18:43
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