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Some Basic References for Dowling Lattices

T. A. Dowling, A class of geometric lattices based on finite groups, J. Combin. Theory, Ser. B 14 (1973) 61-86.

Connections with Coding Theory

T. A. Dowling, Codes, packings and the critical problem, in: Barlotti, ed., ``Atti del Convegno di Geometria Combinatoria e sue Applicazioni,'' (1971) 209-224. Connections with Hyperplane Arrangements

T. Zaslavsky, Facing up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes, AMS Memoirs, v. 1, no. 154 (1975).

T. Zaslavsky, The geometry of root systems and signed graphs, Amer. Math. Monthly, 88 (1981) 88-105.

Axioms and Geometry

J. Bonin and K. Bogart, A geometric characterization of Dowling lattices, J. Combin. Theory, Ser. A 56 (1991) 195-202.

M. K. Bennett, K. Bogart, and J. Bonin, The geometry of Dowling lattices, Advances in Math., 103 (1994) 131-161.

Biased Graphs

T. Zaslavsky, Signed graphs, Disc. Appl. Math. 4 (1982) 47-74.

T. Zaslavsky, Biased graphs. 1. Bias, balance, and gains, J. Combin. Theory, Ser. B 47 (1989) 32-52- - BG 2. The three matroids, J. Combin. Theory, Ser. B 51 (1991) 46-72. - - BG 3. Chromatic and dichromatic invariants, to appear J. Combin. Theory, Ser. B.- - BG 4. Geometrical realizations, to appear J. Combin. Theory, Ser. B

Automorphisms

J. Bonin, Automorphisms of Dowling lattices and related geometries, Combinatorics, Probability, and Computing, 4 (1995) 1-9.

J. Bonin and J. P. S. Kung, Every group is the automorphism group of a rank-3 matroid, Geometriae Dedicata, 50 (1994) 243-246.

Dowling Analogs of the Critical Problem

G. Whittle, Dowling group geometries and the critical problem, J. Combin. Theory, Ser. B 47 (1989) 80-92.

Varieties of Combinatorial Geometries

J. Kahn and J. Kung, Varieties of combinatorial geometries, Trans. Amer. Math. Soc. 271 (1982) 485-499.

J. Kahn and J. Kung, A classification of modularly complemented geometric lattices, European J. Combin. 7 (1986) 243-248.

Algebraic Combinatorics

M. Benoumhani, On Whitney numbers of Dowling lattices, to appear, Disc. Math.

M. Benoumhani, On some numbers related to Whitney numbers of Dowling lattices, to appear, Advances in Applied Math.