On classification of k-dimension paths in n-cube.

Ryabov G.G., Serov V.A.

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) x 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.

Keywords: n-cube, bijection, cubant, k-face, k-path, partition, numerical invariant, Hausdorff-Hamming metrics