On combinatorial arrangements
نویسندگان
چکیده
منابع مشابه
On the Combinatorial Structure of Arrangements of Oriented Pseudocircles
We introduce intersection schemes (a generalization of uniform oriented matroids of rank 3) to describe the combinatorial properties of arrangements of pseudocircles in the plane and on closed orientable surfaces. Similar to the FolkmanLawrence topological representation theorem for oriented matroids we show that there is a one-to-one correspondence between intersection schemes and equivalence ...
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Arrangements are an omni-present topic in computational geometry, since many problems in computer graphics and robotics reduce to the study of such sets. Motivated by two problems from these areas —more precisely from ray-tracing and assembly planning, we study in this paper the combinatorial structure of arrangements of segments on a line and of cones on a circle. We show that the numbers of s...
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Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and reach thereby a weakening of the conditions required to actually determine such orderings. A class of arrangements for which the construction of the minimal comp...
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Given a nonnegative integer m and a finite collection A of linear forms on Qd, the arrangement of affine hyperplanes in Qd defined by the equations α(x) = k for α ∈ A and integers k ∈ [−m,m] is denoted by Am. It is proved that the coefficients of the characteristic polynomial of Am are quasi-polynomials inm and that they satisfy a simple combinatorial reciprocity law.
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A recent progress on the complete enumeration of oriented matroids enables us to generate all combinatorial types of small point configurations and hyperplane arrangements in general dimension, including degenerate ones. This extends a number of former works which concentrated on the non-degenerate case and are usually limited to dimension 2 or 3. Our initial study on the complete list for smal...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1954
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1954-0063332-7