ON THE (n, d)thf-IDEALS

• DOI: 10.4134/jkms.2015.52.4.685
• Publication Date: 2015-07-26T21:38:48Z
• Authors: JIN GUO; TONGSUO WU
• Keywords: Monomial ideal; Degree (music); Square (algebra); Square-free integer

For a field K, square-free monomial ideal I of K[<TEX>$x_1$</TEX>, . ., <TEX>$x_n$</TEX>] is called an f-ideal, if both its facet complex and Stanley-Reisner have the same f-vector. Furthermore, for f-ideal I, all monomials in minimal generating set G(I) degree d, then <TEX>$(n, d)^{th}$</TEX> f-ideal. In this paper, we prove existence <TEX>$d{\geq}2$</TEX> <TEX>$n{\geq}d+2$</TEX>, also give some algorithms to construct f-ideals.