Average order of coloured triangulations: the general case
María Rita Casali · Osaka City University (Osaka City University) · 1998
Theorem 2. [20] Let K be any triangulation of a compact ^-manifold M, with non-empty boundary. Then: (a) 2 < μo(K) < 6, equality holds if and only if K is the triangulation of one 3 -simplex. (b) Ifμo(K) < 3, then K is a triangulation 0/D. (c) Ifμo(K) = 3, then K is a triangulation o/D, D x S, orDx§. (d) For every M and for every rational number r with 3 < r < 6, there exists a triangulation K ofM such that μo(K) = r.