Hexagonal distributions of cities of various sizes in Southern Germany are envisaged in central place theory. Yet scientific verification of this theory has been lacking. To scientifically support this theory, we propose a group-theoretic double Fourier spectrum analysis procedure that can...

Cities in Southern Germany are envisaged to form hexagonal distributions in central place theory; however, rigorous verification of this theory has been lacking over years. To support this theory, we introduce a group-theoretic Fourier spectrum analysis that can detect geometrical patterns of...

We examine an auction model where there are many different goods, each good has multiple units, and bidders have gross substitutes valuations over the goods. We analyze the number of iterations in iterative auction algorithms for the model based on the theory of discrete convex analysis. By...