Inventiones mathematicae

, Volume 68, Issue 2, pp 175–193 | Cite as

Linear diophantine equations and local cohomology

  • Richard P. Stanley

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References

  1. [B-G] Baclawski, K., Garsia, A.M.: Combinatorial decompositions of a class of rings. Advances in Math.39, 155–184 (1981)Google Scholar
  2. [B] Björner, A.: Homotopy type of posets and lattice complementation. J. Combinatorial Theory Ser. A30, 90–100 (1981)Google Scholar
  3. [B-M] Brugesser, H., Mani, P.: Shellable decompositions of cells and spheres. Math. Scand.29, 197–205 (1971)Google Scholar
  4. [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 1963Google Scholar
  5. [F] Folkman, J.: The homology groups of a lattice. J. Math. Mech.15, 631–636 (1966)Google Scholar
  6. [G] Garsia, A.M.: Combinatorial methods in the theory of Cohen-Macaulay rings. Advances in Math.38, 229–266 (1980)Google Scholar
  7. [G-W] Goto, S., Watanabe, K.: On graded rings. II. (Z n-graded rings). Tokyo J. Math.1, 237–261 (1978)Google Scholar
  8. [G-Y] Grace, J.H., Young, A.: The Algebra of Invariants. Cambridge: Cambridge University Press 1903; reprinted by New York: Stechert 1941Google Scholar
  9. [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 1971Google Scholar
  10. [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
  11. [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
  12. [L] Lakser, H.: The homology of a lattice. Discrete Math.1, 187–192 (1971)Google Scholar
  13. [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 1971Google Scholar
  14. [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 1976Google Scholar
  15. [Sp] Spanier, E.H.: Algebraic Topology. New York: McGraw-Hill 1966Google Scholar
  16. [St1] Stanley, R.: Linear homogeneous diophantine equations and magic labelings of graphs. Duke Math. J.40, 607–632 (1973)Google Scholar
  17. [St2] Stanley, R.: Combinatorial reciprocity theorems. Advances in Math.14, 194–253 (1974)Google Scholar
  18. [St3] Stanley, R.: Hilbert functions of graded algebras. Advances in Math.38, 57–83 (1978)Google Scholar
  19. [St4] Stanley, R.: Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (new series)1, 475–511 (1979)Google Scholar
  20. [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 1979Google Scholar
  21. [St6] Stanley, R.: Balanced Cohen-Macaulay complexes. Trans. Amer. Math. Soc.249, 139–157 (1979)Google Scholar
  22. [St7] Stanley, R.: Decompositions of rational convex polytopes. Annals of Discrete Math.6, 333–342 (1980)Google Scholar
  23. [St8] Stanley, R.: Interactions between commutative algebra and combinatorics. Report. U. Stockholm, 1982-No. 4Google Scholar
  24. [W] Walker, J.: Topology and combinatorics of ordered sets. Thesis, M.I.T., 1981Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Richard P. Stanley
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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