[math-fun] Finding equidistant points among the vertices of a cube
Suppose the metric space Q_n is the vertices of the n-dimensional cube Q_n = {-1, 1}^n with the induced metric from Euclidean space, and the questions is: Question: --------- For which n do the points of Q_n include n+1 equidistant points, the maximum possible? (And in general, what is the size S(n) of the largest equidistant subset of Q_n?) If this is in OEIS, I didn't succeed in finding it. —Dan
See https://en.wikipedia.org/wiki/Hadamard_matrix in particular, Sylvester construction. WFL On 8/9/18, Dan Asimov <dasimov@earthlink.net> wrote:
Suppose the metric space Q_n is the vertices of the n-dimensional cube
Q_n = {-1, 1}^n
with the induced metric from Euclidean space, and the questions is:
Question: --------- For which n do the points of Q_n include n+1 equidistant points, the maximum possible?
(And in general, what is the size S(n) of the largest equidistant subset of Q_n?)
If this is in OEIS, I didn't succeed in finding it.
—Dan
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Dan Asimov -
Fred Lunnon