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Generic Cohen-Macaulay Monomial Ideals
Abdul Salam Jarrah1 and Reinhard Laubenbacher2
1Department of Mathematics, East Tennessee State University, Johnson City, TN 37614, USA
2Virginia Bioinformatics Institute, 1880 Pratt Drive, Blacksburg, VA 24061, USA
Annals of Combinatorics 8 (1) p.45-61 March, 2004
AMS Subject Classification: 13P10, 13C14, 52B20, 52B40, 52B22
Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner ideals have Cohen-Macaulay generic deformations. Algorithms are presented to construct such deformations for matroid complexes, shifted complexes, and tree complexes.
Keywords: monomial ideals, simplicial complexes, Cohen-Macaulay


1. D. Bayer, I. Peeva, and B. Sturmfels, Monomial ideals, Math. Res. Lett. 5 (1998) 31–46.

2. L. Billera and A. Björner, Face numbers of polytopes and complexes, In: Discrete and Computational Geometry, J. Goodman and J. O'Rourke, Eds., CRC Press, New York, 1997, pp. 291–310.

3. A. Björner and G. Kalai, On f-vectors and homology, Ann. New York Acad. Sci. 555 (1989) 63–80.

4. G. Kalai, Combinatorics with a geometric flavor: some examples, Geom. Funct. Anal., Special Volume (2000) Part II, 742–791.

5. E. Miller, B. Sturmfels, and K. Yanagawa, Generic and cogeneric monomial ideals, J. Symbolic Comput. 29 (2000) 691–708.

6. J. Oxley, Matroid Theory, Oxford University Press, Oxford, 1992.

7. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann Publications, San Mateo, CA, 1988.

8. R. Stanley, Combinatorics and Commutative Algebra, Progress in Mathematics, Vol. 41, Birkhäuser, Boston, MA, 2 Edition, 1996.

9. R. Stanley, Positivity problems and conjectures in algebraic combinatorics, In: Mathematics: Frontiers and Perspectives V. Arnold, M. Atiyah, P. Lax, and B. Mazur, Eds., Amer. Math. Soc., Providence, RI, 2000, pp. 295–319.

10. K. Yanagawa, fΔ  type free resolutions of monomial ideals, Proc. Amer. Math. Soc. 127 (1998) 37–383.