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%I #25 Mar 09 2022 01:48:08
%S 0,1,0,4,1,0,12,6,1,0,32,36,8,1,0,80,240,100,10,1,0,192,1800,2144,264,
%T 12,1,0,448,15120,80360,22624,672,14,1,0,1024,141120
%N Triangle T(n,k) (0 <= k <= n) giving number of edges in the "flip graph" whose nodes are tilings of the k-dimensional zonotope constructed from n vectors.
%C The zonotope Z(n,k) is the projection of the n-dimensional hypercube onto the k-dimensional space and the tiles are the projections of the k-dimensional faces of the hypercube.
%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 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 N. Destainville, R. Mosseri and F. Bailly, <a href="https://arxiv.org/abs/cond-mat/0004145">Fixed-boundary octagonal random tilings: a combinatorial approach</a>, arXiv:cond-mat/0004145 [cond-mat.stat-mech], 2000.
%H N. Destainville, R. Mosseri and F. Bailly, <a href="https://doi.org/10.1023/A:1026564710037">Fixed-boundary octagonal random tilings: a combinatorial approach</a>, Journal of Statistical Physics, 102 (2001), no. 1-2, 147-190.
%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 0
%e 1 0
%e 4 1 0
%e 12 6 1 0
%e ...
%Y Diagonals give A001787, A001286, A060570, A060608, A060612, A060614, A060616-A060619, A060621-A060624. Cf. A060637.
%K nonn,tabl,hard,more,nice
%O 0,4
%A _N. J. A. Sloane_, Apr 16 2001
%E Edited by _Manfred Scheucher_, Mar 08 2022
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