Polyhedral Subdivisions
and Projections of Polytopes


Jörg Rambau
Dissertation (Advisor: Günter M. Ziegler, TU Berlin)

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Bibliography

1
J. FRANK ADAMS, On the cobar construction, Proceedings of the National Academy of Science 42 (1956), 409-412.

2
LAURA ANDERSON, All euclidean combinatorial differential manifolds are PL manifolds, Preprint, October 1995.

3
ERIC K. BABSON, A combinatorial flag space, Ph.D. thesis, MIT, 1993.

4
EGON BALAS AND MAARTEN OOSTEN, On the dimension of projected polyhedra, Technical Report MSRR-612, Management Science Research Group, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, 1995.

5
HANS JOACHIM BAUES, Geometry of loop spaces and the cobar construction, Memoirs of the American Mathematical Society 25 (1980), 1-171.

6
MARGARET M. BAYER, Equidecomposable and weakly neighborly polytopes, Isreal Journal of Mathematics 81 (1993), 301-320.

7
LOUIS J. BILLERA, PAUL FILLIMAN, AND BERND STURMFELS, Constructions and complexity of secondary polytopes, Advances in Mathematics 83 (1990), 155-179.

8
LOUIS J. BILLERA, ISRAIL M. GELFAND, AND BERND STURMFELS, Duality and minors of secondary polyhedra, Journal of Combinatorial Theory, Series B 57 (1993), 258-268.

9
LOUIS J. BILLERA, MIKHAIL M. KAPRANOV, AND BERND STURMFELS, Cellular strings on polytopes, Proceedings of the American Mathematical Society 122 (1994), 549-555.

10
LOUIS J. BILLERA AND BETH SPELLMAN MUNSON, Triangulations of oriented matroids and convex polytopes, SIAM Journal of Algebraic Discrete Methods 5 (1984), 515-525.

11
LOUIS J. BILLERA AND BERND STURMFELS, Fiber polytopes, Annals of Mathematics 135 (1992), 527-549.

12
LOUIS J. BILLERA AND BERND STURMFELS, Iterated fiber polytopes, Mathematika 41 (1994), 348-363.

13
TIBOR BISZTRICZKY AND GYULA KÁROLYI, Subpolytopes of cyclic polytopes, Preprint, 1995.

14
ANDERS BJÖRNER, Essential chains and homotopy types of posets, Proceedings of the American Mathematical Society 402 (1992), 1179-1181.

15
ANDERS BJÖRNER, MICHEL LAS VERGNAS, BERND STURMFELS, NEIL WHITE, AND GÜNTER M. ZIEGLER, Oriented matroids, Encyclopedia of Mathematics, vol. 46, Cambridge University Press, Cambridge, 1993.

16
JOCHEN BOHNE, Eine kombinatorische Analyse zonotopaler Raumaufteilungen, Preprint 92-041, Sonderforschungsbereich 343 ``Diskrete Strukturen in der Mathematik'', 1992, Dissertation, Fachbereich Mathematik, Universität Bielefeld, 100 pp.

17
GLEN E. BREDON, Topology and Geometry, Graduate Texts in Mathematics, vol. 139, Springer, New York Berlin Heidelberg, 1993.

18
HEINZ BRUGESSER AND PETER MANI, Shellable decompositions of cells and spheres, Mathematica Scandinavica 29 (1971), 197-205.

19
FRANCIS Y. CHIN AND CAO AN WANG, On the difficulty of greedy tetrahedralization of points in 3-d, 7th Canadian Conference on Computational Geometry (Quebec, City), August 1995.

20
THOMAS CHRISTOF, Porta -- a polyhedron representation transformation algorithm (revised by Andreas Loebel and Mechthild Stoer), ZIB electronic library eLib; WWW: http://elib.zib.de; anonymous ftp: ftp://ftp.zib.de/pub/Packages/mathprog/polyth/porta/index .html.

21
PAUL H. EDELMAN AND VICTOR REINER, The higher Stasheff-Tamari posets, Preprint, July 1995, Mathematika, to appear.

22
PAUL H. EDELMAN AND VICTOR REINER, Visibility complexes and the Baues Problem for triangulations in the plane, Preprint, 1995.

23
HERBERT EDELSBRUNNER, Algorithms in Geometry and Topology, Course script 497, University of Illinois, Urbana-Champaign, Spring 1993.

24
HERBERT EDELSBRUNNER AND NIMISH R. SHAH, Incremental topological flipping works for regular triangulations, Proceedings of the 8th annual ACM Symposium on Computational Geometry (Berlin), ACM press, 1992, pp. 43-52.

25
GÜNTER EWALD, Über stellare Äquivalenz konvexer Polytope, Resultate der Mathematik 1 (1978), 54-60.

26
PAUL FILLIMAN, Exterior algebra and projections of polytopes, Discrete & Computational Geometry 5 (1990), 305-322.

27
JON FOLKMAN AND JIM LAWRENCE, Oriented matroids, Journal of Combinatorial Theory, Series B 25 (1978), 199-236.

28
IZRAIL M. GELFAND, MIKHAIL M. KAPRANOV, AND ANDREI V. ZELEVINSKY, Discriminants of polynomials in several variables and triangulations of Newton polyhedra, Leningrad Mathematical Journal 2 (1991), 449-505.

29
IZRAIL M. GELFAND, MIKHAIL M. KAPRANOV, AND ANDREI V. ZELEVINSKY, Discriminants, resultants, and multidimensional determinants, Mathematics: Theory & Applications, Birkhäuser, Boston, 1994.

30
IZRAIL M. GELFAND AND ROBERT D. MACPHERSON, A combinatorial formula for the Pontrjagin classes, Bulletin of the American Mathematical Society 26 (1992), 304-309.

31
WINFRIED GEYER, On Tamari lattices, Discrete Mathematics 133 (1994), 99-122.

32
BRANKO GRÜNBAUM, Convex Polytopes, Interscience, London, 1967.

33
MARK HAIMAN, Constructing the associahedron, Manuscript, unpublished, 1989.

34
SABINE HANKE, THOMAS OTTMANN, AND SVEN SCHUIERER, The edge-flipping distance of triangulations, In Hinrichs [35].

35
KLAUS H. HINRICHS (ed.), Abstracts of the 12th European Workshop on Computational Geometry (CG '96), Report No. 7/96-I, Institut für Informatik, Westfälische Wilhelms-Universität Münster, 1996.

36
SAMUEL HUANG AND DOV TAMARI, Problems of associativity: A simple proof for the lattice property of systems ordered by a semi-associative law, Journal of Combinatorial Theory, Series A 13 (1972), 7-13.

37
FERRAN HURTADO, MARC NOY, AND JORGE URRUTIA, Flipping edges on triangulations, In Hinrichs [35].

38
BARRY JOE, Three dimensional triangulations from local transformations, SIAM Journal of Scientific Statistical Computation 10 (1989), 718-741.

39
BARRY JOE, Construction of three-dimensional Delaunay triangulations using local transformations, Computer Aided Geometric Design 8 (1991), 123-142.

40
MIKHAIL M. KAPRANOV AND VLADIMIR A. VOEVODSKY, Combinatorial-geometric aspects of polycategory theory: pasting schemes and higher Bruhat orders (list of results), Cahiers de Topologie et Géométrie différentielle catégoriques 32 (1991), 11-27.

41
CARL LEE, Triangulations of polytopes, Preprint, July 1995; CRC Handbook of Discrete and Computational Geometry, (Jacob E. Goodman and Joseph O'Rourke, eds.), to appear.

42
CARL LEE, Applied geometry and discrete mathematics: Regular triangulations of convex polytopes, The Victor Klee Festschrift (Peter Gritzmann and Bernd Sturmfels, eds.), American Mathematical Society, Providence, RI, 1991, pp. 443-456.

43
JESÚS A. DE LOERA, Triangulations of polytopes and computational algebra, Ph.D. thesis, Cornell University, 1995.

44
JESÚS A. DE LOERA, Non-regular triangulations of products of simplices, Discrete & Computational Geometry 15 (1996), 253-264.

45
JESÚS A. DE LOERA, SERKAN HOSTEN, FRANCISCO SANTOS, AND BERND STURMFELS, The polytope of all triangulations of a point configuration, Documenta Mathematika 1 (1996), 103-119.

46
LASZLO LOVÁSZ AND ALEXANDER SCHRIJVER, Cones of matrices and set functions and $0$-$1$ optimization, SIAM Journal of Optimization 1 (1991), 166-190.

47
ROBERT D. MACPHERSON, Combinatorial differential manifolds, Topological Methods in Modern Mathematics: A Symposium in Honor of John Milnor's Sixtieth Birthday, Stony Brook NY, 1991 (Lisa R. Goldberg and Anthon V. Phillips, eds.), Publish or Perish, Houston TX, 1993, pp. 203-221.

48
YURII I. MANIN AND VADIM V. SCHECHTMAN, Arrangements of hyperplanes, higher braid groups and higher Bruhat orders, Advanced Studies in Pure Mathematics 17 (1989), 289-308.

49
PETER MCMULLEN, The maximum number of faces of a convex polytope, Mathematika 17 (1970), 179-184.

50
ANDREAS MERTSCH, Triangulierungen und Dreiecks-Bézier-Flächen, Diplomarbeit, Fachbereich Mathematik, Universität Hamburg, 1991.

51
R. JAMES MILGRAM, Iterated loop spaces, Annals of Mathematics 84 (1966), 386-403.

52
JOHN W. MILNOR, Communicated by James D. Stasheff, unpublished.

53
NICOLAI E. MNËV AND JÜRGEN RICHTER-GEBERT, Constructions of oriented matroids with disconnected extension space, Discrete & Computational Geometry 10 (1993), 271-285.

54
NIKOLAI E. MNËV AND GÜNTER M. ZIEGLER, Combinatorial models for the finite-dimensional Grassmannians, Discrete & Computational Geometry 10 (1993), 241-250.

55
ALEXANDER NABUTOVSKY, Extremal triangulations of manifolds, Preprint, 1994.

56
ALEXANDER NABUTOVSKY AND RADEL BEN-AV, Noncomputability arising in dynamical triangulation model of four-dimensional quantum gravity, Communications in Mathematical Physics 157 (1993), 93-98.

57
UDO PACHNER, Bistellare Äquivalenz kombinatorischer Mannigfaltigkeiten, Archiv der Mathematik 30 (1978), 89-98.

58
UDO PACHNER, Über die bistellare Äquivalenz simplizialer Sphären und Polytope, Mathematische Zeitschrift 176 (1981), 565-576.

59
JEAN-MARCEL PALLO, A distance metric on binary trees using lattice-theoretic measures, Information Processing Letters 34 (1990), 113-116.

60
JÖRG RAMBAU, Triangulations of cyclic polytopes and higher Bruhat orders, Preprint 496/1996, Fachbereich Mathematik, TU-Berlin, 1996, Mathematika, to appear.

61
JÖRG RAMBAU AND GÜNTER M. ZIEGLER, Projections of polytopes and the Generalized Baues Conjecture, Preprint 429/1995, Fachbereich Mathematik, TU-Berlin, 1995.

62
VICTOR REINER AND GÜNTER M. ZIEGLER, Coxeter-associahedra, Mathematika 41 (1994), 364-393.

63
JÜRGEN RICHTER-GEBERT, New construction methods for oriented matroids, Ph.D. thesis, Royal Institute of Technology, Department of Mathematics, Stockholm, 1992.

64
JÜRGEN RICHTER-GEBERT AND GÜNTER M. ZIEGLER, Zonotopal tilings and the Bohne-Dress theorem, Proceedings ``Jerusalem Combinatorics '93'' (Helene Barcelo and Gil Kalai, eds.), Contemporary Mathematics, vol. 178, American Mathematical Society, 1994, pp. 211-232.

65
FRANZISCO SANTOS, The polytope of all triangulations of an oriented matroid, Manuscript, March 1996.

66
LUDWIG SCHLÄFLI, Theorie der vielfachen Kontinuität (written 1850-1852), Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, Zürcher and Furrer, Zürich, 1901, pp. 1-237. Reprinted in: Ludwig Schläfli: 1814-1895, Gesammelte Mathematische Abhandlungen, vol. I, Birkhäuser, Basel 1950, pp. 167-387.

67
DANIEL D. SLEATOR, ROBERT E. TARJAN, AND WILLIAM P. THURSTON, Rotation distance, triangulations, and hyperbolic geometry, Journal of the American Mathematical Society 1 (1988), 647-681.

68
RICHARD P. STANLEY, Enumerative Combinatorics, Volume I, Wadsworth & Brooks/Cole, Monterey, 1986.

69
BERND STURMFELS, On the matroid stratification of Grassmann varieties, specialization of coordinates, and a problem of N. White, Advances in Mathematics 75 (1989), 202-211.

70
BERND STURMFELS, Fiber polytopes: A brief overview, Special Differential Equations (Masaaki Yoshida, ed.), Kyushu University, Fukuoka, 1991, pp. 117-124.

71
BERND STURMFELS AND GÜNTER M. ZIEGLER, Extension spaces of oriented matroids, Discrete & Computational Geometry 10 (1993), 23-45.

72
DOV TAMARI, The algebra of bracketings and their enumeration, Nieuw Archief voor Wiskunde X (1962), 131-146.

73
GÜNTER M. ZIEGLER, Shelling polyhedral $3$-balls and $4$-polytopes, Preprint-No. 473/1995, Fachbereich Mathematik, TU-Berlin.

74
GÜNTER M. ZIEGLER, Higher Bruhat orders and cyclic hyperplane arrangements, Topology 32 (1993), 259-279.

75
GÜNTER M. ZIEGLER, Lectures on polytopes, Graduate Texts in Mathematics, vol. 152, Springer, New York, 1995, Updates, Corrections, and more available at http://www.math.tu-berlin.de/~ziegler.



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