Results 31 to 40 of about 25,354 (185)
Stanley depth of squarefree Veronese ideals
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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Degenerations of Monomial Ideals [PDF]
Mathematical Research Letters, 2004 In the paper under review the author describes the degenerations of monomial ideals in \(K[[x,y]]\) with \(\text{ Aut}(K[[x,y]])\)-orbit of dimension at most \(3\). In particular, she determines the monomial ideals that any power of \((x,y^4)\) can degenerate to and makes a conjecture about all the ideals that the powers of \((x,y^4)\) can degenerate ...
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The signature of a monomial ideal
AIMS MathematicsThe irreducible decomposition of a monomial ideal has played an important role in combinatorial commutative algebra, with applications beyond pure mathematics, such as biology.
Jovanny Ibarguen +3 more
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Linear Maps in Minimal Free Resolutions of Stanley-Reisner Rings
Mathematics, 2019 In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex Δ .
Lukas Katthän
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Communications in Algebra, 2013 B. Sturmfels and S. Sullivant associated to any graph a toric ideal, called the cut ideal. We consider monomial cut ideals and we show that their algebraic properties such as the minimal primary decomposition, the property of having a linear resolution or being Cohen--Macaulay may be derived from the combinatorial structure of the graph.
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Random Monomial Ideals: a Macaulay2 package [PDF]
Journal of Software for Algebra and Geometry, 2019 The {\tt Macaulay2} package {\tt RandomMonomialIdeals} provides users with a set of tools that allow for the systematic generation and study of random monomial ideals. It also introduces new objects, Sample and Model, to allow for streamlined handling of random objects and their statistics in {\tt Macaulay2}.
Petrović, Sonja +2 more
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On Characteristic Poset and Stanley Decomposition
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 Let J ⊂ I be two monomial ideals such that I/J is Cohen Macaulay. By associating a finite posets PI/Jg$P_{I/J}^g$ to I/J, we show that if I/J is a Stanley ideal then I/J˜$\widetilde{I/J}$ is also a Stanley ideal, where I/J˜$\widetilde{I/J}$ is the ...
Ahmad Sarfraz +2 more
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On the Stanley depth of powers of some classes of monomial ideals
, 2016 Given arbitrary monomial ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $K$, we investigate the Stanley depth of powers of the sum $I+J$, and their quotient rings, in $A\otimes_K B$ in terms of those of $I$ and $J$.
Cimpoeas, Mircea
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Transversal intersection of monomial ideals [PDF]
Proceedings - Mathematical Sciences, 2019 arXiv admin note: text overlap with arXiv:1611 ...
Saha, Joydip +2 more
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Normality Criteria for Monomial Ideals
Results in Mathematics, 2022 In this paper we study the normality of monomial ideals using linear programming and graph theory. We give normality criteria for monomial ideals, for ideals generated by monomials of degree two, and for edge ideals of graphs and clutters and their ideals of covers.
Luis A. Dupont +2 more
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