AM  Vol.5 No.4 , March 2014
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.
Cite this paper: Ryabov, G. and Serov, V. (2014) On Classification of k-Dimension Paths in n-Cube. Applied Mathematics, 5, 723-727. doi: 10.4236/am.2014.54069.

[1]   Mollard, M. and Ramras, M. (2013) Edge Decompositions of Hypercubes by Paths and by Cycles.

[2]   Mundici, D. (2012) Logic on the n-Cube.

[3]   Leader, I. and Long, E. (2013) Long Geodesics in Subgraphs of the Cube.

[4]   Erde, J. (2013) Decomposing the Cube into Paths.

[5]   Rota, G.-C. and Metropolis, N. (1978) Combinatorial Structure of the Faces of the n-Cube. SIAM Journal on Applied Mathematics, 35, 689-694.

[6]   Stanley, R.P. (1999) Enumerative Combinatorics. Cambridge University Press, Cambridge.

[7]   Manin, Y.I. (1999) Classical Computing, Quantum Computing, and Shor’s Factoring Algorithm.

[8]   Ryabov, G.G. (2009) On the Quaternary Coding of Cubic Structures. (in Russian)

[9]   Ryabov, G.G. (2011) Hausdorff Metric on Faces of the n-Cube. Journal of Mathematical Sciences, 177, 619-622.