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A060597 Number of 6-dimensional tilings of unary zonotopes. The zonotope Z(D,d) is the projection of the D-dimensional hypercube onto the d-dimensional space and the tiles are the projections of the d-dimensional faces of the hypercube. Here d=6 and D varies. 0
1, 2, 16, 1646 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

REFERENCES

A. Bjorner, M. Las Vergnas, B. Sturmfels, N. White and G.M. Ziegler, Oriented Matroids, Encyclopedia of Mathematics 46 Second Edition, Cambridge University Press, 1999

N. Destainville, R. Mosseri and F. Bailly, Fixed-boundary octagonal random tilings: a combinatorial approach, Journal of Statistical Physics, 102 (2001), no. 1-2, 147-190.

Victor Reiner, The generalized Baues problem, in New Perspectives in Algebraic Combinatorics (Berkeley, CA, 1996-1997), 293-336, Math. Sci. Res. Inst. Publ., 38, Cambridge Univ. Press, Cambridge, 1999.

LINKS

Table of n, a(n) for n=6..9.

M. Latapy, Generalized Integer Partitions, Tilings of Zonotopes and Lattices

EXAMPLE

For any d, the only possible tile for Z(d,d) is Z(d,d) itself, therefore the first term of the series is 1. It is well known that there are always two d-tilings of Z(d+1,d), therefore the second term is 2. More examples are available on my web page.

CROSSREFS

Cf. A006245 (two-dimensional tilings), A060595-A060602.

Column k=6 of A060637.

Sequence in context: A125791 A102103 A326974 * A091479 A016031 A001309

Adjacent sequences:  A060594 A060595 A060596 * A060598 A060599 A060600

KEYWORD

nonn,nice

AUTHOR

Matthieu Latapy (latapy(AT)liafa.jussieu.fr), Apr 12 2001

STATUS

approved

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)