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On line arrangements in the hyperbolic plane
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Faculty of Science and Technology, Biology, The Linnaeus Centre for Bioinformatics.
2002 (English)In: European Journal of Combinatorics, Vol. 23, no 5, 549-557 p.Article in journal (Other (popular scientific, debate etc.)) Published
Abstract [en]

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 seta:, it is shown that #L less than or equal to 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 subset of or equal to L', k(L') = k(L) and C(L') = C(L).

Place, publisher, year, edition, pages
2002. Vol. 23, no 5, 549-557 p.
URN: urn:nbn:se:uu:diva-71824OAI: oai:DiVA.org:uu-71824DiVA: diva2:99735
Available from: 2005-05-12 Created: 2005-05-12 Last updated: 2011-01-13

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