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1.
Margherita Barile 《Archiv der Mathematik》2006,87(6):516-521
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 primes.
Received: 12 December 2005 相似文献
2.
We study monomial curves, toric ideals and monomial algebras associated to 4-generated pseudo symmetric numerical semigroups. Namely, we determine indispensable binomials of these toric ideals, give a characterization for these monomial algebras to have strongly indispensable minimal graded free resolutions. We also characterize when the tangent cones of these monomial curves at the origin are Cohen–Macaulay. 相似文献
3.
Daniel Wood 《Journal of Pure and Applied Algebra》2019,223(4):1753-1765
We introduce the notion of a Betti-linear monomial ideal, which generalizes the notion of lattice-linear monomial ideal introduced by Clark. We provide a characterization of Betti-linearity in terms of Tchernev's poset construction. As an application we obtain an explicit canonical construction for the minimal free resolutions of monomial ideals having pure resolutions. 相似文献
4.
Archiv der Mathematik - This paper studies the numbers of minimal generators of powers of monomial ideals in polynomial rings. For a monomial ideal I in two variables, Eliahou, Herzog, and Saem... 相似文献
5.
《代数通讯》2013,41(7):3435-3456
ABSTRACT Heinzer, Mirbagheri, Ratliff, and Shah investigate parametric decomposition of monomial ideals on a regular sequence of a commutative ring R with identity 1 and prove that if every finite intersection of monomial ideals in R is again a monomial ideal, then each monomial ideal has a unique irredundant parametric decomposition. Sturmfels, Trung, and Vogels prove a similar result without the uniqueness. Bayer, Peeva, and Strumfels study generic monomial ideals, that is monomial ideals in the polynomial ring such that no variable appears with the same nonzero exponent in two different minimal generators, and for these ideals they prove the uniqueness of the irredundant irreducible decompositions and give an algorithm to construct this unique irredundant irreducible decomposition. In this paper, we present three algorithms for finding the unique irredundant irreducible decomposition of any monomial ideal. 相似文献
6.
We discuss the linearity of the minimal free resolution of a power of a monomial edge ideal. 相似文献
7.
In this article, we try to understand which generically complete intersection monomial ideals with fixed radical are Cohen–Macaulay. We are able to give a complete characterization for a special class of simplicial complexes, namely the Cohen–Macaulay complexes without cycles in codimension 1. Moreover, we give sufficient conditions when the square-free monomial ideal has minimal multiplicity. 相似文献
8.
For all boundary modules of the Koszul complex of a monomial sequence we construct complexes, which we call Taylor complexes.
For a monomial d-sequences these complexes provide free resolutions of the boundary modules. Let M be the ideal generated by a monomial d-sequence. We use the Taylor complexes to construct minimal free resolutions of the Rees algebra and the associated graded
ring of M.
Received: 13 November 1997 / Revised version: 6 March 1998 相似文献
9.
We characterize componentwise linear monomial ideals with minimal Taylor resolution and consider the lower bound for the Betti
numbers of componentwise linear ideals. 相似文献
10.
Na LeiJunjie Chai Peng XiaYing Li 《Journal of Computational and Applied Mathematics》2011,236(6):1656-1666
Multivariate Birkhoff interpolation is the most complicated polynomial interpolation problem and the theory about it is far from systematic and complete. In this paper we derive an Algorithm B-MB (Birkhoff-Monomial Basis) and prove B-MB giving the minimal interpolation monomial basis w.r.t. the lexicographical order of the multivariate Birkhoff problem. This algorithm is the generalization of Algorithm MB in [L. Cerlinco, M. Mureddu, From algebraic sets to monomial linear bases by means of combinatorial algorithms, Discrete Math. 139 (1995) 73-87] which is a well known fast algorithm used to compute the interpolation monomial basis of the Hermite interpolation problem. 相似文献
11.
《Journal of Computational and Applied Mathematics》2012,236(6):1656-1666
Multivariate Birkhoff interpolation is the most complicated polynomial interpolation problem and the theory about it is far from systematic and complete. In this paper we derive an Algorithm B-MB (Birkhoff-Monomial Basis) and prove B-MB giving the minimal interpolation monomial basis w.r.t. the lexicographical order of the multivariate Birkhoff problem. This algorithm is the generalization of Algorithm MB in [L. Cerlinco, M. Mureddu, From algebraic sets to monomial linear bases by means of combinatorial algorithms, Discrete Math. 139 (1995) 73–87] which is a well known fast algorithm used to compute the interpolation monomial basis of the Hermite interpolation problem. 相似文献
12.
Let S=K[x1,…,xn] be a polynomial ring over a field kand let / be a monomial ideal of S. The main result of this paper is an explicit minimal resolution of kover R= S/Iwhen / is a monomial almost complete intersection ideal of S. We also compute an upper bound on the multigraded resolution of k over a generalization of monomial almost complete intersection ring. 相似文献
13.
14.
《Journal of Pure and Applied Algebra》2022,226(12):107142
We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, and monomial algebras. We analyze them using Strassen's laser method and obtain an upper bound 2.431 on ω. We also explain how in certain monomial cases using the laser method directly is less profitable than first degenerating. Our results form possible paths in the search for valuable tensors for the laser method away from Coppersmith-Winograd tensors. 相似文献
15.
We introduce a monomial ideal whose standard monomials encode the vertices of all fibers of a lattice. We study the minimal generators, the radical, the associated primes and the primary decomposition of this ideal, as well as its relation to initial ideals of lattice ideals. 相似文献
16.
Linear resolutions of quadratic monomial ideals 总被引:1,自引:0,他引:1
We study the minimal free resolution of a quadratic monomial ideal in the case where the resolution is linear. First, we focus on the squarefree case, namely that of an edge ideal. We provide an explicit minimal free resolution under the assumption that the graph associated with the edge ideal satisfies specific combinatorial conditions. In addition, we construct a regular cellular structure on the resolution. Finally, we extend our results to non-squarefree ideals by means of polarization. 相似文献
17.
Margherita Barile 《代数通讯》2013,41(7):2082-2095
We present a class of homogeneous ideals which are generated by monomials and binomials of degree 2 and are set-theoretic complete intersections. This class includes certain reducible varieties of minimal degree and, in particular, the presentation ideals of the fiber cone algebras of monomial varieties of codimension 2. 相似文献
18.
We introduce a specialization technique in order to study monomial ideals that are generated in degree two by using our earlier
results about Ferrers ideals. It allows us to describe explicitly a cellular minimal free resolution of various ideals including
any strongly stable and any squarefree strongly stable ideal whose minimal generators have degree two. In particular, this
shows that threshold graphs can be obtained as specializations of Ferrers graphs, which explains their similar properties. 相似文献
19.
We show that a monomial ideal I in a polynomial ring S has projective dimension ≤ 1 if and only if the minimal free resolution of S∕I is supported on a graph that is a tree. This is done by constructing specific graphs which support the resolution of the S∕I. We also provide a new characterization of quasi-trees, which we use to give a new proof to a result by Herzog, Hibi, and Zheng which characterizes monomial ideals of projective dimension 1 in terms of quasi-trees. 相似文献
20.
Isabella Novik 《Journal of Algebraic Combinatorics》2002,16(1):97-101
We describe a new family of free resolutions for a monomial ideal I, generalizing Lyubeznik's construction. These resolutions are cellular resolutions supported on the rooted complexes of the lcm-lattice of I. Our resolutions are minimal for the matroid ideal of a finite projective space. 相似文献