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On the diffeomorphic type of the complement to a line arrangement in a projective plane

100%

Bogomolov F. , Kulikov V.

Open Mathematics

2012

tom 10

nr 2

521-529

We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011, 45(2), 137–148].

Codes and designs from triangular graphs and their line graphs

60%

Fish W. , Kumwenda K. , Mwambene E.

Open Mathematics

2011

tom 9

nr 6

1411-1423

For any prime p, we consider p-ary linear codes obtained from the span over $\mathbb{F}_p $ p of rows of incidence matrices of triangular graphs, differences of the rows and adjacency matrices of line graphs of triangular graphs. We determine parameters of the codes, minimum words and automorphism groups. We also show that the codes can be used for full permutation decoding.