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A060602 Number of d-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 the codimension, i.e., D-d, is constant = 3 and d varies from 0 to ... 8
8, 24, 62, 148, 338, 752, 1646, 3564, 7658, 16360 (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=0..9.

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


Conjecture: a(n) = 2*(-3+7*2^n+(-1+2^n)*n). G.f.: -2*(4*x^3-11*x^2+12*x-4) / ((x-1)^2*(2*x-1)^2). [Colin Barker, Feb 20 2013]


For any Z(D,d), the number of codimension 0 tilings is always 1, with codimension 1 it is 2, with codimension 2 it is 2.D.


Cf. A006245 (two-dimensional tilings), A060595-A060601. A diagonal of A060637.

Sequence in context: A177719 A317234 A049724 * A066605 A066497 A205963

Adjacent sequences:  A060599 A060600 A060601 * A060603 A060604 A060605




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



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Last modified September 18 04:22 EDT 2021. Contains 347508 sequences. (Running on oeis4.)