Let I\subset S=\KK[x_1,...,x_n] be a lexsegment ideal, generated by
monomials of degree d. The main aim of this paper is to characterize when the
Hilbert depth of I will be 1, in the standard graded case. In addition to
this, we will give an estimate of depth of squarefree monomial ideals,
generalizing a result of Popescu. We will also show that Stanley conjecture
holds for squarefree stable ideals, in the multigraded case.Comment: 14 page