Some Aspects of (Q:X) for Monomial Ideals Q

[[abstract]]For the monomial ideals Q in the polynomial ring k[X1,X2,…,Xd] over a field k, we discuss the minimal monomial generating set of (Q:X), where X=(X1,X2,…,Xd) is the maximal monomial ideal of k[X1,X2,…,Xd]. Moreover, we study (Q:Xs) when s is big enough.