TITLE:
On Classification of k-Dimension Paths in n-Cube
AUTHORS:
G. G. Ryabov, V. A. Serov
KEYWORDS:
n-Cube; Bijection; Cubant; k-Face; k-Path; Partition; Numerical Invariant; Hausdorff-Hamming Metrics
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.4,
March
14,
2014
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.