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ON THE STANLEY DEPTH AND SIZE OF MONOMIAL IDEALS
Glasgow Mathematical Journal, 2017 Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,...,x_n]$ be the polynomial ring in $n$ variables over the field $\mathbb{K}$. For every monomial ideal $I\subset S$, We provide a recursive formula to determine a lower bound for the Stanley depth of $S ...
S. A. Seyed Fakhari
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Stanley depth and Stanley support-regularity of monomial ideals
Collectanea Mathematica, 2016Let \(S=K[x_{1},\dots,x_{n}]\) be a polynomial ring over a field \(K\). Let \(I=\bigcap_{I=1}^{s}\) be an irredundant primary decomposition of a monomial ideal \(I\) in \(S\), where the \(Q_{i}'s\) are also monomial ideals. Lyubeznik acquired that \[ \text{depth}(S/I)\geq\text{siz}(I) \] where \(\text{size}(I)\) is the number \(v+n-h-1\) with \(v\) is ...
Yi-Huang Shen
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Depth and Stanley depth of powers of the path ideal of a cycle graph
Revista de la Unión Matemática Argentina, 2023Let $J_{n,m}:=(x_1x_2\cdots x_m,\; x_2x_3\cdots x_{m+1},\; \ldots,\; x_{n-m+1}\cdots x_n,\; x_{n-m+2}\cdots x_nx_1, \ldots, x_nx_1\cdots x_{m-1})$ be the $m$-path ideal of the cycle graph of length $n$, in the ring $S=K[x_1,\ldots,x_n]$. Let $d=\gcd(n,m)$
Silviu Bălănescu, Mircea Cimpoeaş
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On the depth and Stanley depth of the integral closure of powers of monomial ideals
Collectanea Mathematica, 2018Let \({\mathbb {K}}\) be a field and \(S={\mathbb {K}}[x_1,\ldots ,x_n]\) be the polynomial ring in n variables over \({\mathbb {K}}\). For any monomial ideal I, we denote its integral closure by \({\overline{I}}\).
S. Fakhari
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2013
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 topics of Combinatorial Commutative Algebra: (1) A survey on Stanley decompositions. (2) Generalized Hibi rings and Hibi ideals.
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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 topics of Combinatorial Commutative Algebra: (1) A survey on Stanley decompositions. (2) Generalized Hibi rings and Hibi ideals.
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Stanley depth of weakly 0-decomposable ideals
Archiv der Mathematik, 2014The author provides a new class of monomial ideals which satisfy Stanley's depth conjecture. He shows that weakly \(0\)-decomposable ideals, which include weakly polymatroidal ideals, satisfy Stanley's conjecture (Theorem 2.12). This generalizes a recent result due to \textit{S. A. S. Fakhari} [Arch. Math. 103, No.
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On Stanley Depths of Certain Monomial Factor Algebras
Canadian Mathematical Bulletin, 2015AbstractLet S = K[x1 , . . . , xn] be the polynomial ring in n-variables over a ûeld K and I a monomial ideal of S. According to one standard primary decomposition of I, we get a Stanley decomposition of the monomial factor algebra S/I. Using this Stanley decomposition, one can estimate the Stanley depth of S/I. It is proved that sdepthS(S/I) ≤ sizeS(I)
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Stanley depth of factors of polymatroidal ideals and the edge ideal of forests
Archiv der Mathematik, 2015A. Alipour +2 more
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The fundamentals and applications of ferroelectric HfO2
Nature Reviews Materials, 2022Uwe Schroeder +2 more
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Quantum guidelines for solid-state spin defects
Nature Reviews Materials, 2021Gary Wolfowicz +2 more
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