Monomial ideals induced by permutations avoiding patterns

Let S (or T) be the set of permutations of [n]={1,...,n} avoiding 123 and 132 patterns (or avoiding 123, 132 and 213 patterns). The monomial ideals IS=x sigma=i=1nxi sigma(i):sigma S and IT=x sigma:sigma T in the polynomial ring R=k[x1,...,xn] over a field k have many interesting properties. The Alexander dual IS[n] of IS with respect to n=(n,...,n) has the minimal cellular resolution supported on the order complex (sigma n) of a poset sigma n. The Alexander dual IT[n] also has the minimal cellular resolution supported on the order complex (sigma similar to n) of a poset sigma similar to n. The number of standard monomials of the Artinian quotient RIS[n] is given by the number of irreducible (or indecomposable) permutations of [n+1], while the number of standard monomials of the Artinian quotient RIT[n] is given by the number of permutations of [n+1] having no substring {l,l+1}.