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A060595 Number of 3-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=3 and D varies. 21
1, 2, 10, 148, 7686 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=3..7.

M. Latapy, Tilings of Zonotopes


Z(3,3) is simply a cube and the only possible tile is Z(3,3) 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.


Cf. A006245 (two-dimensional tilings), A060596-A060602.

Column k=3 of A060637.

Sequence in context: A152804 A188490 A213457 * A086619 A194026 A165940

Adjacent sequences:  A060592 A060593 A060594 * A060596 A060597 A060598




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



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Last modified May 23 23:53 EDT 2017. Contains 286937 sequences.