Generic sequences of polynomials

Journal of Algebra

Volumn 324, Issue 4, 2010, Pages 579-590

  Pardue, Keith ^a  

^a NONE

Author keywords

Commutative algebra; Generic properties; Gr bner bases; Hilbert functions

Indexed keywords

EID: 78650738803     PISSN: 00218693     EISSN: 1090266X     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2010.04.018     Document Type: Article

References (24)

1. E. Aguirre, A. Jarrah, R. Laubenbacher, A. Ortiz-Navarro, R. Torrez, Generic initial ideals and the Moreno-Socías Conjecture, in: Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, 2001.
2. Anick D. Thin algebras of embedding dimension three. J. Algebra 1986, 100:235-259.
3. Aubry M. Série de Hilbert d'une algèbre de polynômes quotient. J. Algebra 1995, 176:392-416.
4. Cho Y.H., Park C.P. Conditions for generic initial ideals to be almost reverse lexicographic. J. Algebra 2008, 319:2761-2771.
5. Cimpoeaş M. Generic initial ideal for complete intersections of embedding dimension three with strong Lefschetz property. Bull. Math. Soc. Sci. Math. Roumanie 2007, 50(98):33-66.
6. T. Deery, Stable ideals, resolutions and Betti numbers, Masters Thesis, Queen's University, 1995.
7. Diem C. The XL-algorithm and a conjecture from commutative algebra. Lecture Notes in Comput. Sci. 2004, vol. 3329:146-159. Springer-Verlag.
8. Eisenbud D. Commutative Algebra with a View Toward Algebraic Geometry 1995, Springer-Verlag, New York.
9. Eliahou S., Kervaire M. Minimal resolutions of some monomial ideals. J. Algebra 1990, 129:1-25.
10. Fröberg R. An inequality for Hilbert series of graded algebras. Math. Scand. 1985, 56:117-144.
11. Fröberg R., Hollman J. Hilbert series for ideals generated by generic forms. J. Symbolic Comput. 1994, 17:149-157.
12. Hochster M., Laksov D. The linear syzygies of generic forms. Comm. Algebra 1987, 15:227-239.
13. Iarrobino A. Compressed algebras: Artin algebras having given socle degrees and maximal length. Trans. Amer. Math. Soc. 1984, 285:337-378.
14. Iarrobino A. Inverse system of a symbolic power, III: thin algebras and fat points. Compos. Math. 1997, 108:319-356.
15. Matsumura H. Commutative Algebra 1980, Benjamin/Cummings, Reading, MA.
16. Migliore J., Miró-Roig R.M. Ideals of general forms and the ubiquity of the weak Lefschetz property. J. Pure Appl. Algebra 2003, 182:79-107.
17. G. Moreno-Socías, Autour de la fonction de Hilbert-Samuel (escaliers d'idéaux polynomiaux), Thèse, école Polytechnique, 1991.
18. Moreno-Socías G. Degrevlex Gröbner bases of generic complete intersections. J. Pure Appl. Algebra 2003, 180:263-283.
19. Moreno-Socías G., Snellman J. Some conjectures about the Hilbert series of generic ideals in the exterior algebra. Homology, Homotopy Appl. 2002, 4(2):409-426.
20. Pardue K., Richert B. Syzygies of semi-regular sequences. Illinois J. Math. 2009, 53:349-364.
21. J.P. Park, Almost reverse lexicographic ideals, preprint, 2009.
22. A. Parker, Implications and special cases of the Moreno-Socías conjecture, Senior Thesis, Haverford College, 2002.
23. Stanley R. Weyl groups, the hard Lefschetz theorem and the Sperner property. SIAM J. Alg. Disc. Math. 1980, 1:168-184.
24. Valla G. Problems and results on Hilbert functions of graded algebras. Six Lectures on Commutative Algebra 1991, 293-344. Birkhäuser, Boston.