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Attempts to Count k-Sets

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Part of the Graduate Texts in Mathematics book series (GTM,volume 212)

Abstract

Consider an n-point set X ⊂ R d, and fix an integer k. Call a k-point subset S ⊆ X a k-set of X if there exists an open half-space γ such that S = X ∩ γ; that is, S can be “cut off” by a hyperplane. In this chapter we want to estimate the maximum possible number of k-sets of an n-point set in R d, as a function of n and k.

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© 2002 Springer-Verlag New York, Inc.

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Matoušek, J. (2002). Attempts to Count k-Sets. 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_11

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  • DOI: https://doi.org/10.1007/978-1-4613-0039-7_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-95374-8

  • Online ISBN: 978-1-4613-0039-7

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