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For any positive integer $n$, let $X_n$ be the family of all subsets of $\{1,2,\cdots,n\}$. Let $(X_n,d)$ be the metric space such that $$d(A,B)=|\,A\triangle B\,|,\ \forall A,B\in X_n$$ where $A\...

A polyhedron is the intersection of a finite collection of halfspaces. These halfspaces are not assumed to be linear, i.e. their bounding hyperplanes are not assumed to contain the origin. The ...

I have a N-point metric space defined by the pairwise distance matrix. I want to encode these N points with binary strings, i.e. each point will be mapped to a vertex in a hypercube. The lengths of ...

I want to define a "distance" between two subsets $A, B$ of a normed space $(V, \|\cdot\|)$ both with (at most) $n$ elements. A straightforward way for me to do this would be to define $$ d(A, B) := \...