A060608 Number of flips between the d-dimensional tilings of the unary zonotope Z(D,d). Here d=3 and D varies.

0, 1, 10, 264, 22624

Offset

3,3

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

Table of n, a(n) for n=3..7.

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

Example

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.

Crossrefs

Cf. A001286 (case where d=1). Cf. A060595 (number of 3-tilings) for terminology. A diagonal of A060638.

Sequence in context: A290041 A369423 A160481 * A003388 A322564 A055408

Adjacent sequences: A060605 A060606 A060607 * A060609 A060610 A060611

Keyword

nonn

Author

Matthieu Latapy (latapy(AT)liafa.jussieu.fr), Apr 13 2001

Status

approved