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Expected number of identical vertex pairs with the same Euclidean distance on a randomly colored rectangular lattice
Imagine I have an $N$ by $M$ rectangular lattice where I randomly assign one of $k$ colors to every vertex in the lattice. I then write down a list of the ${N*M}\choose{2}$ possible unordered pairs ...
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16
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4
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The lattice spanned by $m$ random 0-1 vectors of length $n$
Consider $m$ random 0-1 vectors of length $n$. Let $L$ be the lattice spanned by them. What is the value of $m$ (as a function of $n$) for which it is true with positive probability that $L=Z^n$? More ...
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