ON THE (n, d)thf-IDEALS

Abstract

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