Abstract
Let be the polynomial ring in n variables over a field K and I be a monomial ideal of degree . We show that for all and we disprove a motivation question that was asked by of Carlini, Hà, Harbourne and Van Tuyl by providing of a counterexample. Also, by this counterexample, we give a negative answer to the question that the depth function of square-free monomial ideals are non-increasing.
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