Interval sequences and the combinatorial encoding of planar families of pairwise disjoint convex sets
نویسندگان
چکیده
We extend a combinatorial encoding of families of pairwise disjoint convex sets in the plane recently introduced by J. E. Goodman and R. Pollack to the case of families not in general position. This encoding generalizes allowable sequences, which encode finite planar point sets. Further we prove several results on realizability questions, and discuss a number of different combinatorial properties that are captured by this encoding, including a theorem of Helly type and a generalization of a separation result of Tverberg. Supported in part by . †Supported in part by NSA grant H98230-05-1-0082 and PSC-CUNY grant 66496-0035. ‡Supported in part by . §Supported in part by NSF grant CCR-9732101.
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