Attempts to Count k-Sets
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.
KeywordsGeneral Position Middle Level Balance Line Edge Crossing Dual Setting
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