Gaussian paragraphs of pseudolinear arrangements

Jesus Leanos
Maribor University

Drago Bokal
Maribor University



Content: Gauss has given necessary but not sufficient conditions for a sequence of letters to represent the sequence of self-crossings of some closed planar curve. Such sequences of letters were called Gaussian words and recently generalized to Gaussian paragraphs, sets of words that arise from sequences of crossings of several curves. In this talk, we apply Gaussian paragraph representation to pseudo-linear arrangements and present an elementary characterization of pseudo-linear arrangements that can be used to recognize them in time linear in the number of crossings or quadratic in the number of lines. This is an improvement over the only other characterization known to us, which can be verified in time cubic in the number of lines.

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