Results 1 to 10 of about 2,227,707 (156)
On the Stanley Depth of Powers of Monomial Ideals [PDF]
Mathematics, 2019 In 1982, Stanley predicted a combinatorial upper bound for the depth of any finitely generated multigraded module over a polynomial ring. The predicted invariant is now called the Stanley depth. Duval et al.
S. A. Seyed Fakhari
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Depth and Stanley Depth of Multigraded Modules [PDF]
Communications in Algebra, 2010 We study the behavior of depth and Stanley depth along short exact sequences of multigraded modules and under reduction modulo an element.
Asia Rauf
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Stanley depth of squarefree Veronese ideals [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 We compute the Stanley depth for the quotient ring of a square free Veronese ideal and we give some bounds for the Stanley depth of a square free Veronese ideal. In particular, it follows that both satisfy the Stanley's conjecture.
Cimpoeas Mircea
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Upper Bounds for the Stanley Depth [PDF]
Communications in Algebra, 2012 Let $I\subset J$ be monomial ideals of a polynomial algebra $S$ over a field. Then the Stanley depth of $J/I$ is smaller or equal with the Stanley depth of $\sqrt{J}/\sqrt{I}$. We give also an upper bound for the Stanley depth of the intersection of two primary monomial ideals $Q$, $Q'$, which is reached if $Q$, $Q'$ are irreducible, ht$(Q+Q')$ is odd ...
Muhammad Ishaq
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Stanley depth and the lcm-lattice
Journal of Combinatorial Theory - Series A, 2017 In this paper we show that the Stanley depth, as well as the usual depth, are essentially determined by the lcm-lattice. More precisely, we show that for quotients $I/J$ of monomial ideals $J\subset I$, both invariants behave monotonic with respect to certain maps defined on their lcm-lattice. This allows simple and uniform proofs of many new and known
Lukas Katthän +2 more
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Journal of Algebra, 2010 Let $Q$ and $Q'$ be two monomial primary ideals of a polynomial algebra $S$ over a field. We give an upper bound for the Stanley depth of $S/(Q\cap Q')$ which is reached if $Q$,$Q'$ are irreducible. Also we show that Stanley's Conjecture holds for $Q_1\cap Q_2$, $S/(Q_1\cap Q_2\cap Q_3)$, $(Q_i)_i$ being some irreducible monomial ideals of $S$.
Dorin Popescu
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Interval partitions and Stanley depth
Journal of Combinatorial Theory - Series A, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephen Young +2 more
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Depth and Stanley depth of the edge ideals of the powers of paths and cycles [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 Let k be a positive integer. We compute depth and Stanley depth of the quotient ring of the edge ideal associated to the kth power of a path on n vertices.
Iqbal Zahid, Ishaq Muhammad
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The behavior of Stanley depth under polarization
Journal of Combinatorial Theory - Series A, 2015 Version 2: several proofs were clarified and a minor result was added.
Bogdan Ichim
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A variant of the Stanley depth for multisets [PDF]
Discrete Mathematics, 2019 We define and study a variant of the \emph{Stanley depth} which we call \emph{total depth} for partially ordered sets (posets). This total depth is the most natural variant of Stanley depth from $\llbracket S_k\rrbracket$ -- the poset of nonempty subsets of $\{1,2,\dots,k\}$ ordered by inclusion -- to any finite poset.
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