Binomial Ideals

Freiman ideals

“…By Theorem 1.2, in < (J) is squarefree. By [19] (see also [10,Corollary 4.26]) this implies that F (I) is normal. Then by a theorem of Hochster [16] it follows that F (I) is Cohen-Macaulay.…”

Higher Weight Spectra of Veronese Codes

“…This ideal is called the Stanley-Reisner ideal of M and the quotient R M = R/I M the Stanley-Reisner ring associated to M . We refer to [3] for the study of such objects. As described in [8] the Stanley-Reisner ring has minimal N and N n -graded free resolutions…”

Recursive Betti numbers for Cohen–Macaulay d -partite clutters arising from posets

“…Denote by supp(m) the set of variables dividing a monomial m and by G(I) the set of minimal monomial generators of I. If I is a square-free monomial ideal, let I * be its Alexander dual ideal (see for instance [21]).…”

“…Ideals with linear quotients have been introduced by Herzog and Takayama in [22]. For further details see [21] and [23]. Definition 2.3.…”