A060638 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.

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, 12, 1, 0, 448, 15120, 80360, 22624, 672, 14, 1, 0, 1024, 141120

Offset

0,4

Comments

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.

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

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

Table of n, a(n) for n=0..37.

N. Destainville, R. Mosseri and F. Bailly, Fixed-boundary octagonal random tilings: a combinatorial approach, arXiv:cond-mat/0004145 [cond-mat.stat-mech], 2000.

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.

M. Latapy, Generalized Integer Partitions, Tilings of Zonotopes and Lattices, arXiv:math/0008022 [math.CO], 2000.

Example

   0
   1 0
   4 1 0
  12 6 1 0
  ...

Crossrefs

Diagonals give A001787, A001286, A060570, A060608, A060612, A060614, A060616-A060619, A060621-A060624. Cf. A060637.

Sequence in context: A211793 A145880 A048516 * A244125 A007789 A345393

Adjacent sequences: A060635 A060636 A060637 * A060639 A060640 A060641

Keyword

nonn,tabl,hard,more,nice

Author

N. J. A. Sloane, Apr 16 2001

Extensions

Edited by Manfred Scheucher, Mar 08 2022

Status

approved