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On Line Arrangements in the Hyperbolic Plane

✍ Scribed by A. Dress; J.H. Koolen; V. Moulton

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
138 KB
Volume
23
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis

Given a finite collection L of lines in the hyperbolic plane H, we denote by k = k(L) its Karzanov number, i.e., the maximal number of pairwise intersecting lines in L, and by C(L) and n = n(L) the set and the number, respectively, of those points at infinity that are incident with at least one line from L. By using purely combinatorial properties of cyclic sets, it is shown that #L ≀ 2nk -2k+1 2 always holds and that #L equals 2nk -2k+1 2 if and only if there is no collection L of lines in H with L L , k(L ) = k(L) and C(L ) = C(L).

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