A060570 Number of flips between the d-dimensional tilings of the unary zonotope Z(D,d). Here d=2 and D varies.

0, 1, 8, 100, 2144, 80360

Offset

2,3

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=2..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), A006245 (number of 2-tilings). Cf. A060595 (number of 3-tilings) for terminology. A diagonal of A060638.

Sequence in context: A306032 A274844 A302944 * A215875 A317598 A238947

Adjacent sequences: A060567 A060568 A060569 * A060571 A060572 A060573

Keyword

nonn

Author

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

Status

approved