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

Abstract

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.

arXiv comment30 pages, 10 figures, 12 tables. arXiv admin note: text overlap with arXiv:1904.06555

References in corpus (3)

• Weakly modular graphs and nonpositive curvature
• A combinatorial negative curvature condition implying Gromov hyperbolicity
• Lucas sequences in t-uniform simplicial complexes