ACO Seminar

— 4:30pm

Location:
8220 - Wean Hall

Speaker:
Zichao Dong , Doctoral Student,

Convex polytopes in non-elongated point sets in R^d

Abstract:

For any finite point set P⊂Rd, we denote by diam(P) the ratio of the largest to the smallest distances between pairs of points in P. Let cd,α(n) be the largest integer c such that any n-point set P⊂Rd in general position, satisfying diam(P)<αn−−√d (informally speaking, `non-elongated'), contains a convex c-polytope. Valtr proved that c2,α(n)≈n−−√3, which is asymptotically tight in the plane. We generalize the results by establishing cd,α(n)≈nd−1d+1. Along the way we generalize the definitions and analysis of convex cups and caps to higher dimensions, which may be of independent interest. This is a joint work with Boris Bukh.

Event Website:
https://aco.math.cmu.edu/abs-21-22/apr14.html

Contact
Andrew Newman


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