Combinatorial Complexity Bounds for Arrangements of Curves and Surfaces

Kenneth L. Clarkson, Herbert Edelsbrunner

ISBN 10: 1333690045 / ISBN 13: 9781333690045

Verlag: Forgotten Books, 2018

Beschreibung

Print on Demand. This book explores combinatorial distance problems for finite point sets, an intriguing area of mathematical research with a rich history dating back to the 40s. The author presents upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres and similar curves and surfaces, extending previous results in exciting new ways. The book stands out for its clever adaptations of probabilistic counting, Davenport-Schinzel sequences, and elegant geometric and topological arguments. Ultimately, it sheds new light on the interplay between combinatorial arrangements and the distances between objects, offering valuable insights for further research in discrete and computational geometry. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Bestandsnummer des Verkäufers 9781333690045_0

Bibliografische Details

• Titel: Combinatorial Complexity Bounds for Arrangements of Curves and Surfaces
• Verlag: Forgotten Books
• Erscheinungsjahr: 2018
• Sprache: Englisch
• ISBN-10: 1333690045
• ISBN-13: 9781333690045
• Einband: Paperback
• Zustand: New
• Buchtyp: print-on-demand item
• Verkäuferkataloge:
  • Geometry

Über diesen Titel

Inhaltsangabe

Excerpt from Combinatorial Complexity Bounds for Arrangements of Curves and Surfaces

For the case of spheres where the points must be vertices of the arrangement our bound is the first known non-trivial upper bound. No matching lower bound is known if m ens/4, for some constant c. To prove the upper bound for spheres and vertices we derive an extension of an extremum result for bipartite graphs with certain complete subgraphs prohibited (see Lemma this result is of independent interest.

Distance Problems. Using the bounds for incidence problems summarized in Table we derive new bounds for a variety of combinatorial distance problems in two and three dimensions. We first list our results on repeated distances (see Table m denotes the number of points.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.