Grid Orientations, (d,d + 2)-Polytopes, and Arrangements of Pseudolines
نویسندگان
چکیده
منابع مشابه
Grid Orientations, (d, d+2)-Polytopes, and Arrangements of Pseudolines
We investigate the combinatorial structure of linear programs on simple d-polytopes with d + 2 facets. These can be encoded by admissible grid orientations. Admissible grid orientations are also obtained through orientation properties of a planar point configuration or by the dual line arrangement. The point configuration and the polytope corresponding to the same grid are related through an ex...
متن کاملArrangements of double pseudolines
An arrangement of double pseudolines is a finite family of at least two homotopically trivial simple closed curves embedded in the real projective plane, with the property that any two meet exactly four times, at which points they meet transversely, and induce a cell structure on the real projective plane. In this talk I will show that any arrangement of double pseudolines is isomorphic to the ...
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Arrangements of lines and pseudolines are important and appealing objects for research in discrete and computational geometry. We show that there are at most 2 n 2 simple arrangements of n pseudolines in the plane. This improves on previous work by Knuth who proved an upper bound of 3( n 2) ∼= 2 n in 1992 and the first author who obtained 2 n 2 in 1997. The argument uses surprisingly little geo...
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We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory of Ehrhart polynomials to obtain properties of modular and integral flow polynomials. The emphasis is on the geometrical treatment through subgroup arrangeme...
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We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline arrangements, proved in this paper. Counting results derived from an implementation of our algorithm are also reported.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2005
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-005-1187-x