Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-98-12 May 1998

Abstract

We consider the binary constraints formulation of the frequency assignment problem in its most general form: for an arbitrary metric space, with frequencies taking arbitrary real values, and with possibly infinitely many constraints. We obtain some necessary and sufficient conditions for the problem to have a solution with a finite span. When the metric space is the set of integers, we give an exact criterion.

Also we demonstrate a connection of this problem in one-dimensional case with one combinatorial question about finite permutations; and pose some unsolved problems.

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