On Classification of k-Dimension Paths in n-Cube

Abstract

The shortest k-dimension paths (k-paths) between vertices of n-cube are considered on the basis a bijective mapping of k-faces into words over a finite alphabet. The presentation of such paths is proposed as ( n － k + 1)× n matrix of characters from the same alphabet. A classification of the paths is founded on numerical invariant as special partition. The partition consists of n parts, which correspond to columns of the matrix.