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Robin Hartshorne, Connectedness of the Hilbert scheme, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 5–48.
André Galligo, À propos du théorème de-préparation de Weierstrass, Fonctions de plusieurs variables complexes, Lecture Notes in Mathematics Vol. 409, Springer, Berlin, 1974, pp. 543–579.
David Bayer and Michael Stillman, A criterion for detecting m-regularity, Invent. Math. 87 (1987), no. 1, 1–11.
Keith Pardue, Nonstandard Borel-fixed ideals, Ph.D. thesis, Brandeis University, 1994.
David Eisenbud, Commutative algebra, with a view toward algebraic geometry, Graduate Texts in Mathematics Vol. 150, Springer-Verlag, New York, 1995.
Shalom Eliahou and Michel Kervaire, Minimal resolutions of some monomial ideals, J. Algebra 129 (1990), no. 1, 1–25.
Annetta Aramova, Jürgen Herzog, and Takayuki Hibi, Shifting operations and graded Betti numbers, J. Algebr. Combin. 12 (2000), no. 3, 207–222.
Eric Babson, Isabella Novik, and Rekha Thomas, Symmetric iterated Betti numbers, J. Combin. Theory, Ser. A 105 (2004), 233–254.
Anders Björner and Gil Kalai, An extended Euler-Poincaré theorem, Acta Math. 161 (1988), no. 3–4, 279–303.
Anders Björner and Gil Kalai, On f-vectors and homology, Combinatorial Mathematics: Proceedings of the Third International Conference (New York, 1985) (New York), Annals of the New York Academy of Science Vol. 555, New York Academy of Science, 1989, pp. 63–80.
Francis S. Macaulay, Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc. 26 (1927), 531–555.
Anna Maria Bigatti, Upper bounds for the Betti numbers of a given Hilbert function, Commun. Algebra 21 (1993), no. 7, 2317–2334.
Heather A. Hulett, Maximum Betti numbers of homogeneous ideals with a given Hilbert function, Commun. Algebra 21 (1993), no. 7, 2335–2350.
Aldo Conca and Jessica Sidman, Generic initial ideals of points and curves, preprint, 2004. arXiv:math.AC/0402418
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(2005). Borel-fixed monomial ideals. In: Combinatorial Commutative Algebra. Graduate Texts in Mathematics, vol 227. Springer, New York, NY. https://doi.org/10.1007/0-387-27103-1_2
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