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Maximal Betti numbers

Author(s): Marc Chardin; Vesselin Gasharov; Irena Peeva
Journal: Proc. Amer. Math. Soc. 130 (2002), 1877-1880.
MSC (2000): Primary 13D02
Posted: February 4, 2002
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Abstract: We provide a short proof that the lexicographic ideal has the greatest Betti numbers among all graded ideals with a fixed Hilbert function.

References:

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A. Bigatti: Upper bounds for the Betti numbers of a given Hilbert function, Comm. Algebra 21 (1993), 2317-2334. MR 94c:13014

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A. Aramova, L. Avramov, and J. Herzog: Resolutions of monomial ideals and cohomology over exterior algebras, Trans. Amer. Math. Soc. 352 (2000), 579-594. MR 2000c:13021

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A. Aramova, J. Herzog, and T. Hibi: Squarefree lexsegment ideals, Math. Z. 228 (1998), 353-378. MR 99h:13013

[EPY]
D. Eisenbud, S. Popescu, and S. Yuzvinsky: Hyperplane arrangements cohomology and monomials in the exterior algebra, Trans. Amer. Math. Soc., to appear.

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S. Eliahou and M. Kervaire: Minimal resolutions of some monomial ideals, J. Algebra 129 (1990), 1-25. MR 91b:13019

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M. Green: Generic initial ideals, in Six lectures on commutative algebra, Birkhäuser, Progress in Mathematics 166, (1998), 119-185. MR 99m:13040

[Hu]
H. Hulett: Maximum Betti numbers of homogeneous ideals with a given Hilbert function, Comm. Algebra 21 (1993), 2335-2350. MR 94c:13015

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Additional Information:

Marc Chardin
Affiliation: Institut de Mathématiques, UMR 7586 du CNRS, Université Pierre et Marie Curie, F-75252 Paris Cedex 05, France

Vesselin Gasharov
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850

Irena Peeva
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850
Address at time of publication: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

DOI: 10.1090/S0002-9939-02-06471-7
PII: S 0002-9939(02)06471-7
Received by editor(s): June 1, 2000
Posted: February 4, 2002
Communicated by: Michael Stillman
Copyright of article: Copyright 2002, American Mathematical Society

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