Modeling planar configurations

During the part fev ywrr we have introduced two c~binatorial objocte, allovable l equencee and lubda utricee, which encode veriour klndm of geometric informtioa about configurrtlone of points and their dualr, arrangement8 of linea. In the ~88~ of lambda matrices the encoding worke equally well in higher dimnaionr. The kind of Information thst ie encoded, incidence end order propertier, 18 rich enough so thst even though the object 18 mm8 general then 8n l c rum1 configuration it la porrlble (and derirable) to tmnef arm intereating geometric problew Into problw about the object it8elf. In thir way rho object 18 8 “modal” for the geoutrlc configuretion.

[1]  RICHARD P. STANLEY,et al.  On the Number of Reduced Decompositions of Elements of Coxeter Groups , 1984, Eur. J. Comb..

[2]  Richard Pollack,et al.  Helly-Type Theorems for Pseudoline Arrangements in P2 , 1982, J. Comb. Theory, Ser. A.

[3]  Herbert Edelsbrunner,et al.  On the Number of Line Separations of a Finite Set in the Plane , 1985, J. Comb. Theory, Ser. A.

[4]  George B. Purdy,et al.  The Directions Determined by n Points in the Plane , 1979 .

[5]  Raimund Seidel,et al.  Constructing arrangements of lines and hyperplanes with applications , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[6]  Raul Cordovil,et al.  Sur un theoreme de separation des matroïdes orientes de rang trois , 1982, Discret. Math..

[7]  Peter Ungar,et al.  2N Noncollinear Points Determine at Least 2N Directions , 1982, J. Comb. Theory, Ser. A.

[8]  Richard Pollack,et al.  Upper bounds for configurations and polytopes inRd , 1986, Discret. Comput. Geom..

[9]  Noga Alon,et al.  The number of small semispaces of a finite set of points in the plane , 1986, J. Comb. Theory, Ser. A.

[10]  Raul Cordovil,et al.  The directions determined by n points in the plane: a matroidal generalization , 1983, Discret. Math..

[11]  Richard Pollack,et al.  On the Number of k-Subsets of a Set of n Points in the Plane , 1984, J. Comb. Theory, Ser. A.

[12]  Richard Pollack,et al.  On the Combinatorial Classification of Nondegenerate Configurations in the Plane , 1980, J. Comb. Theory, Ser. A.