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Mathematische Zeitschrift

, Volume 178, Issue 1, pp 125–142 | Cite as

On the number of faces of simplicial complexes and the purity of Frobenius

  • Peter Schenzel
Article

Keywords

Simplicial Complex 
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References

  1. 1.
    Baclawski, K.: Whitney numbers of geometric lattices. Advances in Math.16, 125–138 (1975)Google Scholar
  2. 2.
    Baclawski, K.: Galois connections and the Leray spectral sequence. Advances in Math.25, 191–215 (1977)Google Scholar
  3. 3.
    Baclawski, K.: Cohen-Macaulay ordered sets. J. Algebra63, 226–258 (1980)Google Scholar
  4. 4.
    Bruggesser, H., Mani, P.: Shellable decompositions of cells and spheres. Math. Scand.29, 197–205 (1971)Google Scholar
  5. 5.
    Edwards, R.D.: Notices Amer. Math. Soc.22 A, 334 (1975)Google Scholar
  6. 6.
    Grothendieck, A.: Local cohomology. Lecture Notes in Mathematics41. Berlin-Heidelberg-New York: Springer 1967Google Scholar
  7. 7.
    Hartshorne, R.: Residues and duality. Lecture Notes in Mathematics20. Berlin-Heidelberg-New York: Springer 1966Google Scholar
  8. 8.
    Hochster, M.: Cohen-Macaulay rings, combinatorics, and simplicial complexes. Proceedings of the 2nd Oklahoma Ring Theory Conference, 1977, 171–223Google Scholar
  9. 9.
    Hochster, M.: Cyclic purity versus purity in excellent noetherian rings. Trans. Amer. Math. Soc.231, 463–488 (1977)Google Scholar
  10. 10.
    Hochster, M., Roberts, J.L.: The purity of Frobenius and local cohomology. Advances in Math.21, 117–172 (1976)Google Scholar
  11. 11.
    Klee, V.: The number of vertices of a convex polytope. Canad. J. Math.16, 701–720 (1964)Google Scholar
  12. 12.
    McMullen, P.: The maximum number of faces of a convex polytope. Mathematika17, 179–184 (1970)Google Scholar
  13. 13.
    McMullen, P., Shephard, G.C.: Convex polytopes and the Upper Bound Conjecture. London Mathematical Society Lecture Note Series3. Cambridge-London-New York: Cambridge University Press 1971Google Scholar
  14. 14.
    Motzkin, T.S.: Comonotone curves and polyhedra. Bull. Amer. Math. Soc.63, 35 (1957)Google Scholar
  15. 15.
    Munkres, J.: Topological results in combinatorics. PreprintGoogle Scholar
  16. 16.
    Reisner, G.A.: Cohen-Macaulay quotients of polynomial rings. Advances in Math.21, 30–49 (1976)Google Scholar
  17. 17.
    Rota, G.-C.: On the foundations of combinatorial theory I: Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete2, 340–368 (1964)Google Scholar
  18. 18.
    Rudin, M.E.: An unshellable triangulation of a tetrahedron. Bull. Amer. Math. Soc.64, 90–91 (1958)Google Scholar
  19. 19.
    Schenzel, P.: Applications of dualizing complexes to Buchsbaum rings. Advances in Math. (to appear)Google Scholar
  20. 20.
    Schenzel, P.: Local duality without dualizing complexes. PreprintGoogle Scholar
  21. 21.
    Sharp, R.Y.: Dualizing complexes for commutative Noetherian rings. Math. Proc. Cambridge Philos. Soc.78, 369–386 (1975)Google Scholar
  22. 22.
    Spanier, E.H.: Algebraic topology. New York-San Francisco-Toronto-London: McGraw-Hill 1966Google Scholar
  23. 23.
    Stanley, R.P.: The Upper Bound Conjecture and Cohen-Macaulay rings. Studies in Appl. Math.54, 135–142 (1975)Google Scholar
  24. 24.
    Stanley, R.P.: Cohen-Macaulay complexes. In: Higher Combinatorics. Advanced Study Institut Series, 1977, 51–62Google Scholar
  25. 25.
    Stanley, R.P.: Hilbert functions and graded algebras. Advances in Math.28, 57–83 (1978)Google Scholar
  26. 26.
    Stanley, R.P.: Finite lattices and Jordan-Hölder sets. Algebra Universalis4, 361–371 (1974)Google Scholar
  27. 27.
    Stanley, R.P.: Combinatorial reciprocity theorems. Advances in Math.14, 194–253 (1974)Google Scholar
  28. 28.
    Stanley, R.P.: Balanced Cohen-Macaulay complexes. Trans. Amer. Math. Soc.249, 135–157 (1979)Google Scholar
  29. 29.
    Stückrad, J., Vogel, W.: Toward a theory of Buchsbaum singularities. Amer. J. Math.100, 727–746 (1978)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Peter Schenzel
    • 1
  1. 1.Sektion Mathematik der Martin-Luther-Universität Halle-WittenbergHalleGerman Democratic Republic

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