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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)
 OFFSET 3,2 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 Jorge Alberto Olarte, Francisco Santos, Hypersimplicial subdivisions, arXiv:1906.05764 [math.CO], 2019. EXAMPLE 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. CROSSREFS Cf. A006245 (two-dimensional tilings), A060596-A060602. Column k=3 of A060637. Sequence in context: A317075 A295207 A213457 * A303440 A086619 A294373 Adjacent sequences:  A060592 A060593 A060594 * A060596 A060597 A060598 KEYWORD nonn,nice AUTHOR Matthieu Latapy (latapy(AT)liafa.jussieu.fr), Apr 12 2001 STATUS approved

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Last modified February 20 04:12 EST 2020. Contains 332063 sequences. (Running on oeis4.)