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Lexsegment ideals of Hilbert depth 1
Let I\subset S=\KK[x_1,...,x_n] be a lexsegment ideal, generated by
monomials of degree . The main aim of this paper is to characterize when the
Hilbert depth of 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
Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams
We investigate the Castelnuovo--Mumford regularity and the multiplicity of
the toric ring associated to a three-dimensional Ferrers diagram. In
particular, in the rectangular case, we are able to provide direct formulas for
these two important invariants. Then, we compare these invariants for an
accompanied pair of Ferrers diagrams under some mild conditions, and bound the
Castelnuovo--Mumford regularity for more general cases.Comment: 22 pages, 2 figures and comments are welcom
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