Skip to main content

Les arrangements d'hyperplans: Un chapitre de géométrie combinatoire

Part of the Lecture Notes in Mathematics book series (LNM,volume 901)

This is a preview of subscription content, access via your institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie A. Géométrie des hyperplans

  1. R.C. BUCK—Partitions of space, Amer. Math. Monthly, 50(1943), 541–544.

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. B. GÜNBAUM—Convex polytopes, Interscience, New York, 1976.

    Google Scholar 

  3. B. GRÜNBAUM—Arrangements of hyperplanes, Proc. Second Luisiana Conference on Combinatorics, Graph Theory, and Computing, R.C. Mullin and al., ed., Baton Rouge, 1971.

    Google Scholar 

  4. R.O. WINDER—Partitions of N-space by hyperplanes, SIAM J. Appl. Math., 14(1966), 811–818.

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. T. ZASLAVSKY—Facing up to arrangements: face-count formulas for partition of space by hyperplanes, Memoirs Amer. Math. Soc., 154(1975).

    Google Scholar 

B. Matroĩdes

  1. T. BRYLAWSKI—A decomposition for combinatorial geometries, Trans. Amer. Math. Soc., 171(1972), 235–282.

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. H. CRAPO—A higher invariant for matroids, J. Comb. Theory, 2(1967), 406–417.

    MATH  MathSciNet  Google Scholar 

  3. H. CRAPO et G.C. ROTA—On the Foundations of Combinatorial Theory: Combinatorial Geometries, M.I.T. Press, Cambridge, Mass., 1970.

    MATH  Google Scholar 

  4. M. LAS VERGNAS—Convexity in oriented matroids, J. Comb. Theory B, 29(1980), 231–243.

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. G.C. ROTA—On the Foundations of Combinatorial Theory I: Theory of Möbius Functions, Zeit. für Wahrsch., 2(1964), 340–368.

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. W.T. TUTTE—A ring in graph theory, Proc. Cambridge Phil. Soc., 43(1947), 26–40.

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. H. WHITNEY—On the abstract properties of linear dependence, Amer. J. Math., 57 (1935), 509–533.

    CrossRef  MATH  MathSciNet  Google Scholar 

C. Homologie

  1. K. BACLAWSKI—Whitney numbers of geometric lattices, Adv. in Math., 16(1975), 125–138

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. J. FOLKMAN—The homology groups of a lattice, J. Math. and Mech., 15(1966), 631–636.

    MATH  MathSciNet  Google Scholar 

D. Groupes engendrés par des réflexions

  1. V.I. ARNOLD—The cohomology ring of the colored braid group, Mat. Zametki, 5 (1969), 227–231.

    MATH  MathSciNet  Google Scholar 

  2. N. BOURBAKI—Groupes et Algèbres de Lie, chapitres 4 à 6, Hermann, Paris, 1968.

    MATH  Google Scholar 

  3. E. BRIESKORN—Sur les groupes de tresses (d'après V.I. Arnold), Séminaire Bourbaki, 24e année, 1971/2, Lect. Notes 317, Springer, 1973.

    Google Scholar 

  4. P. ORLIK et L. SOLOMON—Combinatorics and topology of complements of hyperplanes, Inv. Math., 56(1980), 167–189.

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. P. ORLIK et L. SOLOMON—Unitary reflection groups and cohomology, Inv. Math., 59(1980), 77–94.

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. K. SAITO—Theory of logarithmic differential forms and logarithmic vector fields, Journ. Fac. Sci. Tokyo IA, 27(1980), 265–291.

    MATH  Google Scholar 

  7. G.C. SHEPHARD et J.A. TODD—Finite unitary reflection groups, Can. J. Math., 6 (1954), 274–304.

    MATH  MathSciNet  Google Scholar 

  8. H. TERAO—Arrangements of hyperplanes and their freeness I; II, Journ. Fac. Sci. Tokyo IA, 27(1980), 293–320.

    MATH  MathSciNet  Google Scholar 

  9. H. TERAO—Generalized exponents of a free arrangement of hyperplanes and Shepherd-Todd-Brieskorn formula, Inv. Math., 63(1981), 159–179.

    CrossRef  MATH  MathSciNet  Google Scholar 

  10. H. TERAO—Free arrangements of hyperplanes and unitary reflection groups, Proc. Japan Acad., 56(1980), 389–392.

    CrossRef  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 N. Bourbaki

About this paper

Cite this paper

Cartier, P. (1981). Les arrangements d'hyperplans: Un chapitre de géométrie combinatoire. In: Séminaire Bourbaki vol. 1980/81 Exposés 561–578. Lecture Notes in Mathematics, vol 901. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097186

Download citation

  • DOI: https://doi.org/10.1007/BFb0097186

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11176-4

  • Online ISBN: 978-3-540-38956-9

  • eBook Packages: Springer Book Archive