Recurrence relations in (s,t)-uniform simplicial complexes

We introduce $(s,t)$-uniform simplicial complexes. We show that the lengths of spheres in minimal filling diagrams associated to loops in such complexes are the terms of certain recurrence relations. We study the limit of the ratio of the area of such spheres over their length as the radii of spheres grow. Besides we compute the average Gaussian curvature for vertices inside these spheres.