Edge Isoperimetric Theorems for Integer Point Arrays

We consider subsets of the n-dimensional grid with the Manhattan metrics, (i.e. the Cartesian product of chains of lengths k1, . . . , kn) and study those of them which have maximal number of induced edges of the grid, and those which are separable from their complement by the least number of edges. The first problem was considered for k1 = · · · = kn by… (More)