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%I #6 Mar 09 2022 09:23:49
%S 0,1,8,100,2144,80360
%N Number of flips between the d-dimensional tilings of the unary zonotope Z(D,d). Here d=2 and D varies.
%D 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.
%D 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.
%D 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.
%H M. Latapy, <a href="https://arxiv.org/abs/math/0008022">Generalized Integer Partitions, Tilings of Zonotopes and Lattices</a>, arXiv:math/0008022 [math.CO], 2000.
%e For any Z(d,d), there is a unique tiling therefore the first term of the series is 0. Likewise, there are always two tilings of Z(d+1,d) with a flip between them, therefore the second term of the series is 1.
%Y Cf. A001286 (case where d=1), A006245 (number of 2-tilings). Cf. A060595 (number of 3-tilings) for terminology. A diagonal of A060638.
%K nonn
%O 2,3
%A Matthieu Latapy (latapy(AT)liafa.jussieu.fr), Apr 13 2001
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