The behavior of Stanley depth under polarization
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Títol
The behavior of Stanley depth under polarizationData de publicació
2015-10Editor
ElsevierCita bibliogràfica
ICHIM, Bogdan; KATTHÄN, Lukas; MOYANO-FERNÁNDEZ, Julio José. The behavior of Stanley depth under polarization. Journal of Combinatorial Theory, Series A, 2015, vol. 135, p. 332-347.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://www.sciencedirect.com/science/article/pii/S0097316515000692Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
Let
K
be
a
field,
R
=
K
[
X
1
,
...,
X
n
]be
the
polynomial
ring
and
J
I
be
two monomial
ideals
in
R
.
In
this
paper
we
show
that
sdepth
I/J
−
depth
I/J
= sdepth
I
p
/J
... [+]
Let
K
be
a
field,
R
=
K
[
X
1
,
...,
X
n
]be
the
polynomial
ring
and
J
I
be
two monomial
ideals
in
R
.
In
this
paper
we
show
that
sdepth
I/J
−
depth
I/J
= sdepth
I
p
/J
p
−
depth
I
p
/J
p
,
where
sdepth
I/J
denotes
the
Stanley
depth
and
I
p
denotes
the
polarization.
This
solves
a
conjecture
by
Herzog
[9]
and
reduces
the
famous
Stanley
conjecture
(for
modules
of
the
form
I/J
)
to
the
squarefree
case.
As
a
consequence,
the
Stanley
conjecture
for
algebras
of
the
form
R/I
and
the
well-
known
combinatorial
conjecture
that
every
Cohen–Macaulay
simplicial
complex
is
partitionable
are
equivalent. [-]
Publicat a
Journal of Combinatorial Theory, Series A Volume 135, October 2015Drets d'accés
© 2015 Elsevier Inc. All rights reserved.
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
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