2024-03-29T10:12:04Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1601742022-11-08T08:27:16Zcom_10234_7037com_10234_9col_10234_8635
Repositori UJI
author
Ichim, Bogdan
author
Katthän, Lukas
author
Moyano-Fernández, Julio José
2016-06-01T09:39:11Z
2016-06-01T09:39:11Z
2015-10
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.
http://hdl.handle.net/10234/160174
http://dx.doi.org/10.1016/j.jcta.2015.05.005
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.
eng
© 2015 Elsevier Inc. All rights reserved.
Monomial ideal
Stanley depth
Stanley decomposition
Poset map
Polarization
The behavior of Stanley depth under polarization
info:eu-repo/semantics/article
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URL
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URL
https://repositori.uji.es/xmlui/bitstream/10234/160174/3/moyano_2015.pdf.txt
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