A survey on Stanley depth
J Herzog - Monomial ideals, computations and applications, 2013 - Springer
At the MONICA conference “MONomial Ideals, Computations and Applications” at the CIEM,
Castro Urdiales (Cantabria, Spain) in July 2011, I gave three lectures covering different …
Castro Urdiales (Cantabria, Spain) in July 2011, I gave three lectures covering different …
Stanley decompositions of modules of covariants
WQ Erickson, M Hunziker - arXiv preprint arXiv:2312.16749, 2023 - arxiv.org
For a complex reductive group $ H $ with finite-dimensional representations $ W $ and $ U
$, the module of covariants for $ W $ of type $ U $ is the space of all $ H $-equivariant …
$, the module of covariants for $ W $ of type $ U $ is the space of all $ H $-equivariant …
A lower bound for depths of powers of edge ideals
L Fouli, S Morey - Journal of Algebraic Combinatorics, 2015 - Springer
Let GG be a graph, and let II be the edge ideal of G G. Our main results in this article provide
lower bounds for the depth of the first three powers of II in terms of the diameter of G G. More …
lower bounds for the depth of the first three powers of II in terms of the diameter of G G. More …
The eventual shape of Betti tables of powers of ideals
Let $ G $ be a finitely generated abelian group, and let $ S= A [x_1,..., x_n] $ be a $ G $-
graded polynomial ring over a commutative ring $ A $. Let $ I_1,..., I_s $ be $ G …
graded polynomial ring over a commutative ring $ A $. Let $ I_1,..., I_s $ be $ G …
[HTML][HTML] The behavior of Stanley depth under polarization
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 …
R. In this paper we show that sdepth I/J− depth I/J= sdepth I p/J p− depth I p/J p, where …
Linear quotients and multigraded shifts of Borel ideals
We investigate whether the property of having linear quotients is inherited by ideals
generated by multigraded shifts of a Borel ideal and a squarefree Borel ideal. We show that …
generated by multigraded shifts of a Borel ideal and a squarefree Borel ideal. We show that …
[图书][B] Monomial ideals, computations and applications
Monomial ideals and algebras are among the simplest structures in commutative algebra
and the main objects in combinatorial commutative algebra. One can highlight several …
and the main objects in combinatorial commutative algebra. One can highlight several …
Upper bounds for the Stanley depth
M Ishaq - Communications in Algebra, 2012 - Taylor & Francis
Let I⊂ J be monomial ideals of a polynomial algebra S over a field. Then the Stanley depth
of J/I is smaller or equal to the Stanley depth of. We give also an upper bound for the Stanley …
of J/I is smaller or equal to the Stanley depth of. We give also an upper bound for the Stanley …
[PDF][PDF] Some algebraic invariants of the edge ideals of perfect [h, d]-ary trees and some unicyclic graphs
T Ayesha, M Ishaq - AIMS Math, 2023 - aimspress.com
This article is mainly concerned with computations of some algebraic invariants of quotient
rings of edge ideals of perfect [h, d]-ary trees and unicyclic graphs. We compute exact values …
rings of edge ideals of perfect [h, d]-ary trees and unicyclic graphs. We compute exact values …
How to compute the multigraded Hilbert depth of a module
B Ichim, JJ Moyano‐Fernández - Mathematische Nachrichten, 2014 - Wiley Online Library
In the first part of this paper we introduce a method for computing Hilbert decompositions
(and consequently the Hilbert depth) of a finitely generated multigraded module M over the …
(and consequently the Hilbert depth) of a finitely generated multigraded module M over the …