Results 101 to 110 of about 887,096 (204)

Regularity of Squarefree Monomial Ideals [PDF]

, 2014
We survey a number of recent studies of the Castelnuovo-Mumford regularity of squarefree monomial ideals. Our focus is on bounds and exact values for the regularity in terms of combinatorial data from associated simplicial complexes and/or hypergraphs.
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Rees cones and monomial rings of matroids [PDF]

, 2008
Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field.
Villarreal, Rafael H.
core   +1 more source

Border Basis of an Ideal of Points and its Application in Experimental Design and Regression

پژوهش‌های ریاضی, 2020
Introduction Border bases are a generalization of Gröbner bases for zero-dimensional ideals which have attracted the interest of many researchers recently. More precisely, border bases provide a new method to find a structurally stable monomial basis for
Samira Poukhajouei, Sare Goli, Amir Hashemi   +2 more
doaj  

An algorithm to compute the Stanley depth of monomial ideals

Le Matematiche, 2008
In this article we describe an algorithm to compute the Stanley depth of I=J where I and J are monomial ideals. We describe also an implementation in CoCoA.
Giancarlo Rinaldo
doaj  

WHEN ARE SYMMETRIC IDEALS MONOMIAL?

Journal of Commutative Algebra, 2023
The notation has been updated and the main result extended; 9 ...
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Monomial Ideals and Planar Graphs [PDF]

, 1999
Grobner basis theory reduces questions about systems of polynomial equations to the combinatorial study of monomial ideals, or staircases. This article gives an elementary introduction to current research in this area. After reviewing the bivariate case, a new correspondence is established between planar graphs and minimal resolutions of monomial ...
Ezra Miller, Bernd Sturmfels
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On Posets, Monomial Ideals, Gorenstein Ideals and their Combinatorics

Order
In this article we first compare the set of elements in the socle of an ideal of a polynomial algebra $K[x_1,\ldots,x_d]$ over a field $K$ that are not in the ideal itself and Macaulay's inverse systems of such polynomial algebras in a purely combinatorial way for monomial ideals, and then develop some closure operational properties for the related ...
Geir Agnarsson, Neil Epstein
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A note on monomial ideals

, 2006
We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms of the number of its minimal monomial generators and the maximum height of its minimal ...
BARILE, Margherita
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Primary decomposition of monomial ideals

, 2001
Let k be a field and R be a polynomial ring in n variables over k. Every ideal I of R=k[x₁, ... ,x_n]can be written as a finite intersection of primary ideals. A monomial ideal is an ideal of k[x₁, ...
장보금
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Powers of Monomial Ideals

, 1999
We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer.
Haynes, Rhonda S.
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