Generalized triangulations and diagonal-free subsets of stack polyominoes
Journal of Combinatorial Theory Series A
A bijection between 2-triangulations and pairs of non-crossing Dyck paths
Journal of Combinatorial Theory Series A
Fast distance multiplication of unit-Monge matrices
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A new perspective on k-triangulations
Journal of Combinatorial Theory Series A
The brick polytope of a sorting network
European Journal of Combinatorics
Subword complexes, cluster complexes, and generalized multi-associahedra
Journal of Algebraic Combinatorics: An International Journal
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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 ⊊ ⊆ Lt, k(Lt) = k(L) and C(Lt) = C(L).