For any integer r 2, define a sequence of numbers {c (r) k }k=0,1,..., independent of the parameter n, by n k=0 n k r n + k k r = n k=0 n k n + k k c (r) k , n = 0, 1, 2, . . . ....
A configuration (pq, nk) is a collection of p points and n straight lines in the Euclidean plane so that every point has q straight lines passing through it and every line has k p...
The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the p...