Let $ d >0 $ be an integer, and let $ I \subset K[x_1,...x_n] $ be a monomial ideal.
$ I = ( x_1^{a_1}x_2^{a_2}...x_n^{a_n} : \ \sum_{i=1}^n a_i =d; \ a_i < d \forall i)$.
(a) Compute the saturation $ \widetilde{I} $.
(b) The smallest integer $ k $ such that $ I : m^k = I : m^{k+1} $ is called the saturation number of $ I $. What is the saturation number of $ I $?
$ m = (x_1,...,x_n) $
The saturation $ \widetilde{I} $ of $ I $ is the ideal $ I : m^{\infty} = \cup_{k=1}^{\infty} I : m^k$
