Results 31 to 40 of about 25,379 (179)
Integer sequences and monomial ideals
Proceedings - Mathematical Sciences, 2021 Let $\mathfrak{S}_n$ be the set of all permutations of $[n]=\{1,\ldots,n\}$ and let $W$ be the subset consisting of permutations $σ\in \mathfrak{S}_n$ avoiding 132 and 312-patterns. The monomial ideal $I_W = \left\langle \mathbf{x}^σ = \prod_{i=1}^n x_i^{σ(i)} : σ\in W \right\rangle $ in the polynomial ring $R = k[x_1,\ldots,x_n]$ over a field $k$ is ...
Kumar, Chanchal, Roy, Amit
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Mathematics, 2022 In 1974, the author proved that the codimension of the ideal (g1,g2,…,gd) generated in the group algebra K[Zd] over a field K of characteristic 0 by generic Laurent polynomials having the same Newton polytope Γ is equal to d!×Volume(Γ).
Anatoly Kushnirenko
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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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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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Cohen-Macaulay and (S2) Properties of the Second Power of Squarefree Monomial Ideals
Mathematics, 2019 We show that Cohen-Macaulay and (S 2 ) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal I such that S / I 2 satisfies the Serre condition (S 2 ), but is ...
Do Trong Hoang +2 more
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Some Results On Normal Homogeneous Ideals
, 2002 In this article we investigate when a homogeneous ideal in a graded ring is normal, that is, when all positive powers of the ideal are integrally closed.
Reid, Les +2 more
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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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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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