Skip to main content
Log in

Linear diophantine equations and local cohomology

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [B-G] Baclawski, K., Garsia, A.M.: Combinatorial decompositions of a class of rings. Advances in Math.39, 155–184 (1981)

    Google Scholar 

  • [B] Björner, A.: Homotopy type of posets and lattice complementation. J. Combinatorial Theory Ser. A30, 90–100 (1981)

    Google Scholar 

  • [B-M] Brugesser, H., Mani, P.: Shellable decompositions of cells and spheres. Math. Scand.29, 197–205 (1971)

    Google Scholar 

  • [C-S] Chomsky, N., Schützenberger, M.-P.: The algebraic theory of context-free languages. In: Computer programming and formal systems (Braffort, P., Hirschberg, D., eds.). Amsterdam: North-Holland Publications 1963

    Google Scholar 

  • [F] Folkman, J.: The homology groups of a lattice. J. Math. Mech.15, 631–636 (1966)

    Google Scholar 

  • [G] Garsia, A.M.: Combinatorial methods in the theory of Cohen-Macaulay rings. Advances in Math.38, 229–266 (1980)

    Google Scholar 

  • [G-W] Goto, S., Watanabe, K.: On graded rings. II. (Z n-graded rings). Tokyo J. Math.1, 237–261 (1978)

    Google Scholar 

  • [G-Y] Grace, J.H., Young, A.: The Algebra of Invariants. Cambridge: Cambridge University Press 1903; reprinted by New York: Stechert 1941

    Google Scholar 

  • [H-K] Herzog, J., Kunz, E. (eds.): Der kanonische Modul eines Cohen-Macaulay-Rings. Lecture Notes in Math. vol. 238. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  • [H] Hochster, M.: Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes. Ann. of Math.96, 318–337 (1972)

    Google Scholar 

  • [H-R] Hochster, M., Roberts, J.L.: Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay. Advances in Math.13, 115–175 (1974)

    Google Scholar 

  • [L] Lakser, H.: The homology of a lattice. Discrete Math.1, 187–192 (1971)

    Google Scholar 

  • [M-S] McMullen, P., Shephard, G.C.: Convex polytopes and the upper bound conjecture. London Math. Soc. Lecture Note Series, vol. 3. Cambridge: Cambridge University Press 1971

    Google Scholar 

  • [M] Mumford, D.: Hilbert's fourteenth problem-the finite generation of subrings such as rings of invariants. In: Mathematical developments arising from Hilbert problems (Browder, F., ed.). Proc. Symposia Pure Math., vol. 28, pp. 431–444. Providence, R.I.: American Mathematical Society 1976

    Google Scholar 

  • [Sp] Spanier, E.H.: Algebraic Topology. New York: McGraw-Hill 1966

    Google Scholar 

  • [St1] Stanley, R.: Linear homogeneous diophantine equations and magic labelings of graphs. Duke Math. J.40, 607–632 (1973)

    Google Scholar 

  • [St2] Stanley, R.: Combinatorial reciprocity theorems. Advances in Math.14, 194–253 (1974)

    Google Scholar 

  • [St3] Stanley, R.: Hilbert functions of graded algebras. Advances in Math.38, 57–83 (1978)

    Google Scholar 

  • [St4] Stanley, R.: Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (new series)1, 475–511 (1979)

    Google Scholar 

  • [St5] Stanley, R.: Combinatorics and invariant theory. In: Relations between combinatorics and other parts of mathematics (Ray-Chaudhuri, D.K., ed.). Proc. Symposia in Pure Math., vol. 34, pp. 345–355. Providence, R.I.: American Mathematicals Society 1979

    Google Scholar 

  • [St6] Stanley, R.: Balanced Cohen-Macaulay complexes. Trans. Amer. Math. Soc.249, 139–157 (1979)

    Google Scholar 

  • [St7] Stanley, R.: Decompositions of rational convex polytopes. Annals of Discrete Math.6, 333–342 (1980)

    Google Scholar 

  • [St8] Stanley, R.: Interactions between commutative algebra and combinatorics. Report. U. Stockholm, 1982-No. 4

  • [W] Walker, J.: Topology and combinatorics of ordered sets. Thesis, M.I.T., 1981

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stanley, R.P. Linear diophantine equations and local cohomology. Invent Math 68, 175–193 (1982). https://doi.org/10.1007/BF01394054

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01394054

Keywords

Navigation