A060621 Number of flips between the d-dimensional tilings of the unary zonotope Z(D,d). Here the codimension D-d is equal to 3 and d varies.

12, 36, 100, 264, 672, 1664, 4032, 9600, 22528, 52224

Offset: 0

Author

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

Keywords

• nonn

Examples

			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.
		

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

• M. Latapy, Generalized Integer Partitions, Tilings of Zonotopes and Lattices

Crossrefs

Cf. A060595 (number of 3-tilings) for terminology. A diagonal of A060638.

Formula

Numbers so far satisfy a(n) = 2^n*(n^2+11n+24)/2. - Ralf Stephan, Apr 08 2004

Empirical g.f.: -4*(7*x^2-9*x+3) / (2*x-1)^3. - Colin Barker, Feb 20 2013