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A Golomb ruler is a sequence of integers whose pairwise differences, orequivalently pairwise sums, are all distinct. This definition has beengeneralized in various ways to allow for sums of h integers, or to allow up tog repetitions of a given sum or difference. Beck, Bogart, and Pham applied thetheory of inside-out polytopes of Beck and Zaslavsky to prove structuralresults about the counting functions of Golomb rulers. We extend their approachto the various types of generalized Golomb rulers.

An Ehrhart theoretic approach to generalized Golomb rulers