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Deletion-Induced Triangulations, Clifford T. Taylor

Theses and Dissertations--Mathematics

Let d > 0 be a fixed integer and let A ⊆ ℝ^d be a collection of n ≥ d + 2 points which we lift into ℝ^d+1. Further let k be an integer satisfying 0 ≤ k ≤ n-(d+2) and assign to each k-subset of the points of A a (regular) triangulation obtained by deleting the specified k-subset and projecting down the lower hull of the convex hull of the resulting lifting. Next, for each triangulation we form the characteristic vector defined by Gelfand, Kapranov, and Zelevinsky by assigning to each …