Certain variants of multipermutohedron ideals

Integer Sequences and Monomial Ideals

“…Proof. Standard monomials of R I W (u) [un] are characterized in Theorem 4.3 of [6]. Proceeding on similar lines, we get the desired result.…”

“…Clearly, |W | = 2 n−1 . The monomial ideal I W appeared in [6], where it is called a hypercubic ideal. Many properties of I W and its Alexander dual…”

“…Using the cellular resolution of I W (u) [un+c−1] supported on the order complex ∆(Σ n ), we obtain the multigraded Hilbert series −1] . Proceeding as in the proof of Proposition 4.5 of [6], we get a combinatorial formula −1] , where µ u j,Aq is as in Proposition 2.1. Let C be a chain in Σ n of the form…”

“…, x , and applying L'Hospital's rule, we get the first formula. For more detail, see the proof of Proposition 4.5 of [6]. In order to get the second formula, put y j = 1…”

“…[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]. The standard monomials of R I…”