A partition theorem for Euclidean $n$-space

@inproceedings{Samelson1958APT,
  title={A partition theorem for Euclidean \$n\$-space},
  author={Hans Samelson and Robert M. Thrall and Oscar Wesler},
  year={1958}
}
Let Vn be an n-dimensional vector space over the reals. Let s . . ' Sins 7)1, * * I, nbe 2n vectors in Vn such that every sequence of vectors { a,, , an }, where ai is either ti or vi, is a linearly independent set. Let (a,, * *, I n) denote the cone spanned by these a's, i.e. the set of all linlear combinations of the ai with non-negative coefficients. The 2n cones in Vn spanlned by the 2n such sequences of a's will be said to partition Vn if their union is all of Vn and if the intersection of… 
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