Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

ALGORITHMS FOR MINIMAL FREE RESOLUTIONS HAVING MAXIMAL POSSIBLE BETTI NUMBERS

  • Shin, Yong-Su (Department of Mathematics, Sungshin Women's University)
  • Published : 2004.05.01

⟨ Previous Next ⟩

Abstract

We introduce several algorithms for adding up Artinian O-sequences to obtain the maximal possible Betti numbers among all minimal free resolutions with the given Hilbert function. Moreover, we give open questions based on the outputs using those algorithms.

Keywords

References

  1. Communications in Algebra v.21 no.7 Upper Bounds for the Betti Numbers of a Given Hubert Fnnction A. M. Bigatti
  2. Lecture Notes in Math. v.1092 Compressed Algebras, Complete Intersections (Acireale, 1983) F. Froberg;D. Laksov
  3. Illinois J. of Math. v.45 no.1 An Alternative to the Hubert function for the ideal of a finite set of points in $\mathbb{P}^n$ A. V. Geramia;T. Harima;Y. S. Shin
  4. Adv. in Math. v.152 Extremal point sets and Gorenstein ideals A.V. Geramita;T. Harima;Y.S. Shin
  5. J. of Alg. v.268 Some Special Configurations of Points in $\mathbb{P}^n$ A.V. Geramita;T. Harima;Y.S. Shin
  6. J. of Pure and App. AIg. v.122 Smooth Points of Qor(T) A.V. Geramita;M. Pucci;Y.S. Shin
  7. J. of Alg. v.213 k-configurations in $\mathbb{P}^3$ All Have ExtremaL Resolutions A.V. Geramita;Y.S. Shin
  8. J. of Pure and App. Alg. v.103 Some Examples of unimodal Gorenstein sequences T. Harima
  9. Communications in Algebra v.21 no.7 Maximum Betti Numbers of Homogeneous Ideals with a Given Hilbert Function H.A. Hulett
  10. Illinois J. of Math. v.40 Deformation Classes of Graded Modules and Maximal Betti Numbers K. Pardue
  11. Available via anonymous ftp from cocoa.unige. it CoCoA, a system for doing Computations in Commutative Algebra L. Robbiano;J. Abbott;A. Bigatti;M. Caboara;D. Perkinson;V. Augustin;A.Wills
  12. J. Appl. Math. & Computing v.11 no.1-2 Some Construction of All Level Artinian 0-sequences of Socle Degree 5 and Type 3 D.S. Shin;Y.S. Shin
  13. S-PLUS 2000 Professional Release 2