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    Lexsegment ideals of Hilbert depth 1

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    Let I\subset S=\KK[x_1,...,x_n] be a lexsegment ideal, generated by monomials of degree dd. The main aim of this paper is to characterize when the Hilbert depth of II 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
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