We study the problem of the maximum number of unit distances among n points in the plane, under the additional restriction that we count only those unit distances that occur in a fixed set of k directions, taking the maximum over all sets of n points and all sets of k directions. We prove that, for fixed k and sufficiently large n > n0(k) , the extremal sets are essentially sections of lattices, bounded by edges parallel to the k directions and of equal length.    26 June, 1998  Editors-in-Chief: la href=../edboard.html#chiefslJacob E. Goodman, Richard Pollackl/al  19n3p355.pdf  yes  no  no  yes
['Peter Braß']
On Point Sets with Many Unit Distances in Few Directions