Snake

A simple circuit in the -Hypercube which has no chords (i.e., for which all snake edges are edges of theHypercube). Klee (1970) asked for the maximum length of a -snake. Klee (1970) gave the bounds

(1)

(2)

(3)

(4)

References

Abbott, H. L. and Katchalski, M. ``On the Snake in the Box Problem.'' J. Combin. Th. Ser. B 44, 12-24, 1988.

Danzer, L. and Klee, V. ``Length of Snakes in Boxes.'' J. Combin. Th. 2, 258-265, 1967.

Douglas, R. J. ``Some Results on the Maximum Length of Circuits of Spread in the -Cube.'' J. Combin. Th. 6, 323-339, 1969.

Evdokimov, A. A. ``Maximal Length of a Chain in a Unit -Dimensional Cube.'' Mat. Zametki 6, 309-319, 1969.

Guy, R. K. ``Unsolved Problems Come of Age.'' Amer. Math. Monthly 96, 903-909, 1989.

Kautz, W. H. ``Unit-Distance Error-Checking Codes.'' IRE Trans. Elect. Comput. 7, 177-180, 1958.

Klee, V. ``What is the Maximum Length of a -Dimensional Snake?'' Amer. Math. Monthly 77, 63-65, 1970.

Sloane, N. J. A. SequenceA000937/M0995in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

Snevily, H. S. ``The Snake-in-the-Box Problem: A New Upper Bound.'' Disc. Math. 133, 307-314, 1994.

• Fundamental Theorem of Arithmetic
• Fundamental Theorem of Curves
• Fundamental Theorem of Directly Similar Figures
• Fundamental Theorem of Gaussian Quadrature
• Fundamental Theorem of Genera
• Fundamental Theorem of Plane Curves
• Fundamental Theorem of Projective Geometry
• Fundamental Theorem of Space Curves
• Fundamental Theorem of Symmetric Functions
• Fundamental Theorems of Calculus
• Fundamental Unit
• Funnel
• Fuss's Problem
• Futile Game
• Fuzzy Logic
• FWHM
• Gabriel's Horn
• Gabriel's Staircase
• Gadget
• Gale-Ryser Theorem
• Galilean Transformation
• Gallows
• Gall's Stereographic Projection
• Gallucci's Theorem
• Galois Extension Field