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DCG
2007
79views more  DCG 2007»
15 years 4 months ago
Distance Measures for Well-Distributed Sets
In this paper we investigate the Erd¨os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We pr...
Alex Iosevich, Michael Rudnev
COMBINATORICA
2004
69views more  COMBINATORICA 2004»
15 years 4 months ago
Structural Results For Planar Sets With Many Similar Subsets
Consider a k-element subset P of the plane. It is known that the maximum number of sets similar to P that can be found among n points in the plane is (n2 ) if and only if the cros...
Bernardo M. Ábrego, György Elekes, Sil...
JCT
2010
77views more  JCT 2010»
15 years 2 months ago
Obtainable sizes of topologies on finite sets
We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ...
Kári Ragnarsson, Bridget Eileen Tenner
APAL
2004
132views more  APAL 2004»
15 years 4 months ago
Canonical structure in the universe of set theory: part one
Abstract. We start by studying the relationship between two invariants isolated by Shelah, the sets of good and approachable points. As part of our study of these invariants, we pr...
James Cummings, Matthew Foreman, Menachem Magidor
CVBIA
2005
Springer
15 years 10 months ago
Active Contours Under Topology Control Genus Preserving Level Sets
We present a novel framework to exert topology control over a level set evolution. Level set methods offer several advantages over parametric active contours, in particular automat...
Florent Ségonne, Jean-Philippe Pons, W. Eri...