Abstract
We give a sharp lower bound for the Hilbert function in degree d of artinian quotients Bbbk [x_1,ldots ,x_n]/I failing the Strong Lefschetz property, where I is a monomial ideal generated in degree d ge 2. We also provide sharp lower bounds for other classes of ideals, and connect our result to the classification of the Hilbert functions forcing the Strong Lefschetz property by Zanello and Zylinski.
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