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COMBINATORICA
2011
12 years 10 months ago
2011
Thomassen [Combinatorica 24 (2004), 699–718] proved that a 2–connected, compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it doe...
COMBINATORICA
2011
12 years 10 months ago
2011
Let L be a finite distributive lattice and µ : L → R+ a logsupermodular function. For functions k : L → R+ let Eµ(k; q) def = x∈L k(x)µ(x)qrank(x) ∈ R+ [q]. We prove fo...
COMBINATORICA
2011
12 years 10 months ago
2011
We prove several quantitative Ramseyan results involving ternary complete trees with {0, 1}-labeled edges where we attempt to find a complete binary subtree with as few labels as ...
COMBINATORICA
2011
12 years 10 months ago
2011
The topological Tverberg theorem states that for any prime power q and continuous map from a (d + 1)(q − 1)-simplex to Rd , there are q disjoint faces Fi of the simplex whose im...
COMBINATORICA
2011
12 years 10 months ago
2011
Given independent random points X1, . . . , Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n) > 0, we construct a random geometric graph Gn wi...