Given an rc-complex K and a vertex v in K, the ndegree of v is the number of n-simplexes in K containing t7. The set of all Ti-degrees in a complex K is called its n-degree sequence when arranged in nonincreasing order. The question "Which sequences of integers are ndegree sequences?" is answered in this paper. This is done by generalizing the iterative characterization for the 1-dimensional (graphical) case due to V. Havel. A corollary to this general theorem yields the analogous… CONTINUE READING