Source list for Math 8680: Topics in combinatorics
Arrangements of hyperplanes and subspaces

Spring 2000


Arrangements of hyperplanes, P. Orlik and H. Terao, Springer-Verlag 1992.


Orlik, Peter Introduction to arrangements. CBMS Regional Conference Series in Mathematics, 72. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1989.

Falk, Michael; Randell, Richard On the homotopy theory of arrangements. Complex analytic singularities, 101--124, Adv. Stud. Pure Math., 8, North-Holland, Amsterdam-New York, 1987.

Falk, Michael; Randell, Richard On the homotopy theory of arrangements, II. Available at

Wagner, Dave An introduction to arrangements of hyperplanes. Notes for lectures at Queen's University, January 11-13, 1999. Available at

Denham, Graham: Hanlon Phil Some algebraic properties of the Schechtman-Varchenko bilinear forms in "New Perspectives in Geometric Combinatorics", MSRI Publications, 38 (1999) 149--175

Varchenko, Alexandre Multidimensional hypergeometric functions in conformal field theory, algebraic $K$-theory, algebraic geometry. Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 281--300, Math. Soc. Japan, Tokyo, 1991

Brylawski, Thomas; Oxley, James The Tutte polynomial and its applications. Matroid applications, 123--225, Encyclopedia Math. Appl., 40, Cambridge Univ. Press, Cambridge, 1992.

Sagan, Bruce E. Why the characteristic polynomial factors. Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 2, 113--133.

Björner, Anders Subspace arrangements. First European Congress of Mathematics, Vol. I (Paris, 1992), 321--370, Progr. Math., 119, Birkhäuser, Basel, 1994.

Björner, Anders Nonpure shellability, f-vectors, subspace arrangements and complexity. Formal power series and algebraic combinatorics (New Brunswick, NJ, 1994), 25--53, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 24, Amer. Math. Soc., Providence, RI, 1996.

Björner, Anders The homology and shellability of matroids and geometric lattices. Matroid applications, 226--283, Encyclopedia Math. Appl., 40, Cambridge Univ. Press, Cambridge, 1992.

Athanasiadis, Christos Deformations of Coxeter hyperplane arrangements and their characteristic polynomials< Preprint, November 1998, 26 pages, in ``Arrangements - Tokyo 1998'' (M. Falk and H. Terao, eds.), Advanced Studies in Pure Mathematics, to appear. Available at

Zaslavsky, Thomas The Möbius function and the characteristic polynomial. Combinatorial geometries. 114--138, Encyclopedia Math. Appl., 29, Cambridge Univ. Press, Cambridge, 1987

More focussed papers:

Bidigare, Pat; Hanlon, Phil; Rockmore, Dan; A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements. Duke Math. J. 99 (1999), no. 1, 135--174.

Brown, Kenneth S.; Diaconis, Persi; Random walks and hyperplane arrangements. Ann. Probab. 26 (1998), no. 4, 1813--1854.

Billera, Louis J.; Ehrenborg, Richard; Readdy, Margaret The $c$-$2d$-index of oriented matroids. J. Combin. Theory Ser. A 80 (1997), no. 1, 79--105.

Bayer, Margaret M.; Brandt, Keith A. Discriminantal arrangements, fiber polytopes and formality. J. Algebraic Combin. 6 (1997), no. 3, 229--246. Denham, Graham; Hanlon, Phil On the Smith normal form of the Varchenko bilinear form of a hyperplane arrangement. Olga Taussky-Todd: in memoriam. Pacific J. Math. 1997, Special Issue, 123--146.

Athanasiadis, Christos A. Characteristic polynomials of subspace arrangements and finite fields. Adv. Math. 122 (1996), no. 2, 193--233.

Blass, Andreas; Sagan, Bruce Eli Bijective proofs of two broken circuit theorems. J. Graph Theory 10 (1986), no. 1, 15--21.

Edelman, Paul H. A partial order on the regions of ${R}\sp{n}$ dissected by hyperplanes. Trans. Amer. Math. Soc. 283 (1984), no. 2, 617--631.

Greene, Curtis; Zaslavsky, Thomas On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs. Trans. Amer. Math. Soc. 280 (1983), no. 1, 97--126. McMullen, Peter Volumes of projections of unit cubes. Bull. London Math. Soc. 16 (1984), no. 3, 278--280.

McMullen, P. Convex bodies which tile space. The geometric vein, pp. 123--128, Springer, New York-Berlin, 1981.

Björner, Anders; Ekedahl, Torsten Subspace arrangements over finite fields: cohomological and enumerative aspects. Adv. Math. 129 (1997), no. 2, 159--187.

Björner, Anders; Edelman, Paul H.; Ziegler, Günter M. Hyperplane arrangements with a lattice of regions. Discrete Comput. Geom. 5 (1990), no. 3, 263--288.

Björner, Anders; Ziegler, Günter M. Combinatorial stratification of complex arrangements. J. Amer. Math. Soc. 5 (1992), no. 1, 105--149.

Björner, Anders; Lovász, László. Linear decision trees, subspace arrangements and Möbius functions. J. Amer. Math. Soc. 7 (1994), no. 3, 677--706.

Ziegler, Günter M.; Zivaljevic, Rade T. Homotopy types of subspace arrangements via diagrams of spaces. Math. Ann. 295 (1993), no. 3, 527--548.

Richter-Gebert, Jürgen; Ziegler, Günter M. Zonotopal tilings and the Bohne-Dress theorem. Jerusalem combinatorics '93, 211--232, Contemp. Math., 178, Amer. Math. Soc., Providence, RI, 1994.

Massey, David B.; Simion, Rodica; Stanley, Richard P.; Vertigan, Dirk; Welsh, Dominic J. A.; Ziegler, Günter M. Lê numbers of arrangements and matroid identities. J. Combin. Theory Ser. B 70 (1997), no. 1, 118--133.

Feichtner, Eva Maria; Ziegler, Günter M. On cohomology algebras of complex subspace arrangements. Trans. Amer. Math. Soc., to appear.

Falk, Michael The minimal model of the complement of an arrangement of hyperplanes. Trans. Amer. Math. Soc. 309 (1988), no. 2, 543--556.

Falk, Michael Arrangements and cohomology. Ann. Comb. 1 (1997), no. 2, 135--157.

Falk, Michael; Randell, Richard The lower central series of a fiber-type arrangement. Invent. Math. 82 (1985), no. 1, 77--88.

Varchenko, Alexandre Bilinear form of real configuration of hyperplanes. Adv. Math. 97 (1993), no. 1, 110--144.

Varchenko, A. N.; Gelfand, I. M. Heaviside functions of a configuration of hyperplanes. (Russian) Funktsional. Anal. i Prilozhen. 21 (1987), no. 4, 1--18, 96. English translation: Functional Anal. Appl. 21 (1987), no. 4, 255--270.

Hanlon, Phil; Stanley, Richard P.; A $q$-deformation of a trivial symmetric group action. Trans. Amer. Math. Soc. 350 (1998), no. 11, 4445--4459.

Edelman, P. H.; Reiner, V. Free arrangements and rhombic tilings. Discrete Comput. Geom. 15 (1996), no. 3, 307--340.

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