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Generic and cogeneric monomial ideals

Publication ,  Journal Article
Miller, E; Sturmfels, B; Yanagawa, K
Published in: Journal of Symbolic Computation
January 1, 2000

Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions encoded by simplicial complexes. There are numerous equivalent ways to say that a monomial ideal is generic or cogeneric. For a generic monomial ideal, the associated primes satisfy a saturated chain condition, and the Cohen-Macaulay property implies shellability for both the Scarf complex and the Stanley-Reisner complex. Reverse lexicographic initial ideals of generic lattice ideals are generic. Cohen-Macaulayness for cogeneric ideals is characterized combinatorially; in the cogeneric case, the Cohen-Macaulay type is greater than or equal to the number of irreducible components. Methods of proof include Alexander duality and Stanley's theory of local h -vectors. © 2000 Academic Press.

Duke Scholars

Published In

Journal of Symbolic Computation

DOI

ISSN

0747-7171

Publication Date

January 1, 2000

Volume

29

Issue

4-5

Start / End Page

691 / 708

Related Subject Headings

  • General Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Miller, E., Sturmfels, B., & Yanagawa, K. (2000). Generic and cogeneric monomial ideals. Journal of Symbolic Computation, 29(4–5), 691–708. https://doi.org/10.1006/jsco.1999.0290
Miller, E., B. Sturmfels, and K. Yanagawa. “Generic and cogeneric monomial ideals.” Journal of Symbolic Computation 29, no. 4–5 (January 1, 2000): 691–708. https://doi.org/10.1006/jsco.1999.0290.
Miller E, Sturmfels B, Yanagawa K. Generic and cogeneric monomial ideals. Journal of Symbolic Computation. 2000 Jan 1;29(4–5):691–708.
Miller, E., et al. “Generic and cogeneric monomial ideals.” Journal of Symbolic Computation, vol. 29, no. 4–5, Jan. 2000, pp. 691–708. Scopus, doi:10.1006/jsco.1999.0290.
Miller E, Sturmfels B, Yanagawa K. Generic and cogeneric monomial ideals. Journal of Symbolic Computation. 2000 Jan 1;29(4–5):691–708.
Journal cover image

Published In

Journal of Symbolic Computation

DOI

ISSN

0747-7171

Publication Date

January 1, 2000

Volume

29

Issue

4-5

Start / End Page

691 / 708

Related Subject Headings

  • General Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics