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ON THE CONNECTIVITY NUMBERS OF LINEARLY SEPARABLE SETS
LOCKHEED MISSILES AND SPACE CO SUNNYVALE CALIF
A formula for certain invariants the connectivity differences associated with the points of canonical linearly separable sets of the unit hypercube is derived. These may be used to derive the connectivity numbers of any linearly separable set. It is also proved that for less than 5, or equal to the connectivity numbers uniquely define a canonical linearly separable set while for n less than or equal to 6, they do not. Some investigation is made of sets of points which can be added to a canonical set to produce two different canonical sets with the same connectivities. Also presented is a simple formulation of the number of line-segments of the unit hypercube which is entirely in a given canonical linearly separable set n, and of the number of such line-segments cut by every hyperplane which separates this set from the other points of the unit hypercube. Author