Results 31 to 40 of about 177 (175)

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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MONOMIAL IDEALS FROM A SEMIRING PERSPECTIVE

Tạp chí Khoa học Đại học Đà Lạt
We formulate the theory of monomial ideals of a ring of polynomials with coefficients in a field through the theory of semirings. In particular, we focus on the theory of integrally closed monomial ideals.
Cristhian Garay-López, P. Rubí Pantaleón-Mondragón, Saúl Aranda   +2 more
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A remark on sequentially Cohen-Macaulay monomial ideals [PDF]

Transactions on Combinatorics
Let $R=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. We show that if $G$ is a connected graph with a basic $5$-cycle $C$, then $G$ is a sequentially Cohen-Macaulay graph if and only if there exists a shedding vertex $x$ of $
Mozhgan Koolani, Amir Mafi
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When Is a Graded Free Complex Exact?

Mathematics, 2022
Minimal free resolutions of a finitely generated module over a polynomial ring S=k[x], with variables x={x1,…,xn} and a field k have been extensively studied.
David C. Molano, Javier A. Moreno, Carlos E. Valencia   +2 more
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Monomial Cut Ideals

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, Stasi, Despina, Wilburne, Dane   +2 more
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Hadamard Product of Monomial Ideals and the Hadamard Package

Mathematics
In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and ...
Iman Bahmani Jafarloo, Cristiano Bocci, Elena Guardo   +2 more
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A note on minimal resolutions of vector–spread Borel ideals

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
We consider vector–spread Borel ideals. We show that these ideals have linear quotients and thereby we determine the graded Betti numbers and the bigraded Poincaré series.
Crupi Marilena, Ficarra Antonino
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Transversal intersection of monomial ideals [PDF]

Proceedings - Mathematical Sciences, 2019
arXiv admin note: text overlap with arXiv:1611 ...
Saha, Joydip, Sengupta, Indranath, Tripathi, Gaurab   +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, Humberto Muñoz-George, Rafael H. Villarreal   +2 more
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