Heawood's empire problem

The Empire Problem in Penrose Tilings

Nonperiodic tilings of the plane exhibit no translational symmetry. Penrose tilings are a remarkable class of nonperiodic tilings for which the set of prototiles consists of just two shapes. The pentagrid method, introduced by N.G. de Bruijn, allows us to generate Penrose tilings by taking a slice of the integer lattice in five-dimensional space. The empire problem asks: Given a subset of a Pen...

Complexity Results for the Empire Problem in Collection of Stars

In this paper, we study the Empire Problem, a generalization of the coloring problem to maps on two-dimensional compact surface whose genus is positive. Given a planar graph with a certain partition of the vertices into blocks of size r, for a given integer r, the problem consists of deciding if s colors are sufficient to color the vertices of the graph such that vertices of the same block have...

Racism, Empire and Sociology

‘[T]he entity called Europe was constructed from the outside in as much as from the inside out.’ So wrote Mary Louise Pratt, at the start of Imperial Eyes (1992: 6), her insightful account of colonial travelogue. Pratt’s point provides a pithy summary of one of the central claims of what was, at the time, the still emerging field of postcolonial studies (in which context, of course, Imperial Ey...

The British Empire Exhibition

Regeneration through Empire