Abstract
This is a continuation of the chapter on arrangements. We again study the number of vertices in a certain part of the arrangement: the lower envelope. Already for segments in the plane, this problem has an unexpectedly subtle and difficult answer. The closely related combinatorial notion of Davenport-Schinzel sequences has proved to be a useful general tool, since the surprising phenomena encountered in the analysis of the lower envelope of segments are by no means rare in combinatorics and discrete geometry.
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© 2002 Springer-Verlag New York, Inc.
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Matoušek, J. (2002). Lower Envelopes. In: Matoušek, J. (eds) Lectures on Discrete Geometry. Graduate Texts in Mathematics, vol 212. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0039-7_7
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DOI: https://doi.org/10.1007/978-1-4613-0039-7_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95374-8
Online ISBN: 978-1-4613-0039-7
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