Monomial ideals induced by permutations avoiding patterns

Integer Sequences and Monomial Ideals

“…S of I S is an order monomial ideal for S = S n (132, 231), S n (123, 132) and S n (123, 132, 213) (see [7,8]). The minimal generators of I W (u) [un+c−1] correspond to elements of poset Σ n .…”

“…for S = S n (132, 231), S n (123, 132) and S n (123, 132, 213) are give in [7,8]. In this section, the monomial ideal I S and its Alexander dual I…”

“…S (see Proposition 5.23 of [9]). Now proceeding as in the proof of Lemma 2.1 and 2.2 of [8], it is easy to get the minimal generators of the Alexander duals. We sketch a proof of part (i) and (vi) as proof of other parts are on similar lines.…”

“…Sa is an order monomial ideal. Postnikov and Shapiro [12] showed that the free complex F * (∆(P )) is a cellular resolution of the order monomial ideal I = ω u : u ∈ P (see Theorem 2.4 of [8]).…”

“…[n] S for subsets S = S n (132, 231), S n (123, 132) and S n (123, 132, 213) are obtained in [7,8] Let W = S n (132, 312). The monomial ideal I W of R is called a hypercubic ideal in [6].…”