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Monomial ideals
 Mathematical Computations with Macaulay 2
, 2002
"... Monomial ideals form an important link between commutative algebra and combinatorics. In this chapter, we demonstrate how to implement algorithms in Macaulay 2 for studying and using monomial ideals. We illustrate these methods with examples from combinatorics, integer programming, and algebraic geo ..."
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Cited by 16 (2 self)
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Monomial ideals form an important link between commutative algebra and combinatorics. In this chapter, we demonstrate how to implement algorithms in Macaulay 2 for studying and using monomial ideals. We illustrate these methods with examples from combinatorics, integer programming, and algebraic
On the radical of a monomial ideal
 J. ALGEBRA
, 2004
"... Algebraic and combinatorial properties of a monomial ideal and its radical are compared. ..."
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Cited by 61 (9 self)
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Algebraic and combinatorial properties of a monomial ideal and its radical are compared.
Multiplier ideals of monomial ideals
 Trans. Amer. Math. Soc
"... Abstract. In this note we discuss a simple algebraic calculation of the multiplier ideal associated to a monomial ideal in affine nspace. We indicate how this result allows one to compute not only the multiplier ideal but also the log canonical threshold of an ideal in terms of its Newton polygon. ..."
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Cited by 75 (1 self)
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Abstract. In this note we discuss a simple algebraic calculation of the multiplier ideal associated to a monomial ideal in affine nspace. We indicate how this result allows one to compute not only the multiplier ideal but also the log canonical threshold of an ideal in terms of its Newton polygon.
Some Normal Monomial Ideals
, 2002
"... Abstract. In this paper we investigate the question of normality for special monomial ideals in a polynomial ring over a field. We first include some expository sections that give the basics on the integral closure of a ideal, the Rees algebra on an ideal, and some fundamental results on the integra ..."
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Cited by 2 (1 self)
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Abstract. In this paper we investigate the question of normality for special monomial ideals in a polynomial ring over a field. We first include some expository sections that give the basics on the integral closure of a ideal, the Rees algebra on an ideal, and some fundamental results
BLOWUPS IN TAME MONOMIAL IDEALS
, 2009
"... We study blowups of affine nspace with center an arbitrary monomial ideal and call monomial ideals that render smooth blowups tame ideals. We give a combinatorial criterion to decide whether the blowup is smooth and apply this criterion to discuss a smoothing procedure proposed by Rosenberg, mono ..."
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Cited by 1 (0 self)
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We study blowups of affine nspace with center an arbitrary monomial ideal and call monomial ideals that render smooth blowups tame ideals. We give a combinatorial criterion to decide whether the blowup is smooth and apply this criterion to discuss a smoothing procedure proposed by Rosenberg
Monomial ideals and planar graphs
 APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERRORCORRECTING CODES, VOLUME 1719 OF SPRINGER LECTURE NOTES IN COMPUTER SCIENCE
, 1999
"... Gröbner 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 ..."
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Cited by 3 (0 self)
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Gröbner 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
The jmultiplicity of monomial ideals
 GROWTH OF MULTIPLICITIES OF GRADED FAMILIES OF IDEALS 11
"... Abstract. We prove a characterization of the jmultiplicity of a monomial ideal as the normalized volume of a polytopal complex. Our result is an extension of Teissier’s volumetheoretic interpretation of the HilbertSamuel multiplicity for mprimary monomial ideals. We also give a description of ..."
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Cited by 3 (2 self)
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Abstract. We prove a characterization of the jmultiplicity of a monomial ideal as the normalized volume of a polytopal complex. Our result is an extension of Teissier’s volumetheoretic interpretation of the HilbertSamuel multiplicity for mprimary monomial ideals. We also give a description
Antichains of monomial ideals are finite
 Proc. Amer. Math. Soc
, 2001
"... The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already posets is shown to be false. ..."
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Cited by 24 (6 self)
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The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already posets is shown to be false.
A note on monomial ideals
, 2005
"... 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 maximal height of its minimal primes. ..."
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Cited by 4 (3 self)
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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 maximal height of its minimal primes.
REGULARITY OF SQUAREFREE MONOMIAL IDEALS
, 2013
"... We survey a number of recent studies of the CastelnuovoMumford 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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Cited by 5 (0 self)
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We survey a number of recent studies of the CastelnuovoMumford 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.
Results 1  10
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