Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Characterization of Hilbert functions of Gorenstein Artin algebras with the weak Stanley property


Author: Tadahito Harima
Journal: Proc. Amer. Math. Soc. 123 (1995), 3631-3638
MSC: Primary 13D40; Secondary 13C40, 13H10, 14M06
DOI: https://doi.org/10.1090/S0002-9939-1995-1307527-7
MathSciNet review: 1307527
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a characterization of Hilbert functions of Gorenstein Artin algebras with the weak Stanley property. Namely, we prove that a necessary and sufficient condition for a given O-sequence $ \underline H $ to be the Hilbert function of some Gorenstein Artin algebra with the weak Stanley property is that the sequence $ \underline H $ is an SI-sequence.


References [Enhancements On Off] (What's this?)

  • [1] D. Bernstein and A. Iarrobino, A nonunimodal graded Gorenstein Artin algebra in codimension five, Comm. Algebra 20 (1992), 2323-2336. MR 1172667 (93i:13012)
  • [2] L. J. Billera and C. W. Lee, Sufficiency of McMullen's conditions for f-vectors of simplicial polytopes, Bull. Amer. Math. Soc. (N.S.) 2 (1980), 181-185. MR 551759 (81b:52004)
  • [3] M. Boij and D. Laksov, Nonunimodality of graded Gorenstein Artin algebras, Proc. Amer. Math. Soc. 120 (1994), 1083-1092. MR 1227512 (94g:13008)
  • [4] E. D. Davis, A. V. Geramita, and F. Orecchia, Gorenstein algebras and the Cayley-Bacharach theorem, Proc. Amer. Math. Soc. 93 (1985), 593-597. MR 776185 (86k:14034)
  • [5] A. V. Geramita, D. Gregory, and L. Roberts, Monomial ideals and points in projective space, J. Pure Appl. Algebra 40 (1986), 33-62. MR 825180 (87d:13023)
  • [6] A. V. Geramita, P. Maroscia, and L. Roberts, The Hilbert function of a reduced k-algebra, The Curves Seminar at Queen's Vol. II, Queen's Papers in Pure and Appl. Math., vol. 61, Queen's Univ., Kingston, Ontario, 1982. MR 783087 (86g:13014)
  • [7] F. S. Macaulay, Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc. (3) 26 (1927), 531-555.
  • [8] C. Peskine and L. Szpiro, Liaison des variétés algébriques. I, Invent. Math. 26 (1974), 271-302. MR 0364271 (51:526)
  • [9] A. Sodhi, On the intersection of a hypersurface with a finite set of points in $ {{\mathbf{P}}^n}$, J. Pure Appl. Algebra 74 (1991), 85-94. MR 1129132 (93d:14080)
  • [10] R. Stanley, Cohen-Macaulay rings and constructible polytopes, Bull. Amer. Math. Soc. 81 (1975), 133-135. MR 0364231 (51:486)
  • [11] -, Hilbert functions of graded algebras, Adv. in Math. 28 (1978), 57-83. MR 0485835 (58:5637)
  • [12] -, The number of faces of a simplicial convex polytope, Adv. in Math. 35 (1980), 236-238. MR 563925 (81f:52014)
  • [13] J. Watanabe, The Dilworth number of Artinian rings and finite posets with rank function, Commutative Algebra and Combinatorics, Adv. Stud. Pure Math., vol. 11, Academic Press, Boston, MA, 1987, pp. 303-312. MR 951211 (89k:13015)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13D40, 13C40, 13H10, 14M06

Retrieve articles in all journals with MSC: 13D40, 13C40, 13H10, 14M06


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1307527-7
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society