Median calculation for heterogeneous complex of abstract cubes

Abstract

Median problem for an arbitrary complex of abstract cubes is studied. First, a number of auxiliary results related to some special metric properties of abstract $n$-dimensional cube are presented. Basing on these results and results obtained in the study of homogeneous complexes [13], it is proved that median of an arbitrary complex of abstract cubes can be calculated without using metrics. Method which represents a generalization of method applied to homogeneous complex of abstract cubes is proposed.

Keywords

• Abstract cube
• cubic complex
• median
• transversal
• group of homologies
• convex set
• class of parallel edges