Acknowledgement
Supported by : Kongju National University
References
- D. Bernstein and A. Iarrobino, A non-unimodal graded Gorenstein Artin algebra in codimension five, Comm. Algebra 20 (1992), no. 8, 2323-2336. https://doi.org/10.1080/00927879208824466
- A. M. Bigatti and A. V. Geramita, Level Algebras, Lex Segments and Minimal Hilbert Functions, Comm. Algebra 31 (2003), 1427-1451. https://doi.org/10.1081/AGB-120017774
- M. Boij, Graded Gorenstein Artin algebras whose Hilbert functions have a large number of valleys, Comm. Algebra 23 (1995), no. 1, 97-103. https://doi.org/10.1080/00927879508825208
- W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge studies in advanced Mathematics, 39, Revised edition (1998), Cambridge, U.K.
- M. Boij and D. Laksov, Nonunimodality of graded Gorenstein Artin algebras, Proc. Amer. Math. Soc. 120 (1994), no. 4, 1083-1092. https://doi.org/10.1090/S0002-9939-1994-1227512-2
- M. Green. Restrictions of linear series to hyperplanes, and some results of Macaulay and Gotzmann. In Algebraic curves and projective geometry (Trento, 1988), volume 1389 of Lecture Notes in Math., pages 76-86. Springer, Berlin, 1989.
- M. Kreuzer and L. Robbiano. Computational commutative algebra. 2. Springer-Verlag, Berlin, 2005.
- F. S. Macaulay, The algebraic theory of modular systems, Revised reprint of the 1916 original. With an introduction by Paul Roberts. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1994.
- J. Migliore, U. Nagel, and F. Zanello, Bounds and asymptotic minimal growth for Gorenstein Hilbert functions, J. Algebra 321 (2009), no. 5, 1510-1521. https://doi.org/10.1016/j.jalgebra.2008.11.026
- J. Migliore, U. Nagel, and F. Zanello, On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley, Proc. Amer. Math. Soc. 136 (2008), no. 8, 2755-2762. https://doi.org/10.1090/S0002-9939-08-09456-2
- R. P. Stanley, Hilbert functions of graded algebras, Advances in Math. 28 (1978), no. 1, 57-83. https://doi.org/10.1016/0001-8708(78)90045-2
- F. Zanello, Stanley's theorem on codimension 3 Gorenstein h-vectors, Proc. Amer. Math. Soc. 134 (2006), no. 1, 5-8 (electronic) https://doi.org/10.1090/S0002-9939-05-08276-6
- J. Migliore(1-NDM), U. Nagel(1-KY), and F. Zanello(1-NDM), On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley. (English sum- mary) Proc. Amer. Math. Soc. 136 (2008), no. 8, 2755-2762. https://doi.org/10.1090/S0002-9939-08-09456-2