A351383 Number of tilings of the d-dimensional zonotope constructed from d+4 vectors.

16, 120, 908, 7686, 78032, 1000488, 16930560, 393454160, 12954016496, 613773463394

Offset: 0

Author

Manfred Scheucher, Feb 09 2022

Keywords

• nonn
• hard
• more

Comments

The zonotope Z(D,d) is the projection of the D-dimensional hypercube onto the d-dimensional space and the tiles are the projections of the d-dimensional faces of the hypercube. Here the codimension, i.e., D-d, is constant = 4 and d >= 0.

Also the number of signotopes on r+3 elements of rank r. A signotope on n elements of rank r is a mapping X:{{1..n} choose r}->{+,-} such that for any r+1 indices I={i_0,...,i_r} with i_0 < i_1 < ... < i_r, the sequence X(I-i_0), X(I-i_1), ..., X(I-i_r) changes its sign at most once (see Felsner-Weil reference).

Links

• S. Felsner and H. Weil, Sweeps, arrangements and signotopes, Discrete Applied Mathematics, Volume 109, Issues 1-2, 2001, Pages 67-94.
• M. Latapy, Generalized Integer Partitions, Tilings of Zonotopes and Lattices, arXiv:math/0008022 [math.CO], 2000.
• G. M. Ziegler, Higher Bruhat Orders and Cyclic Hyperplane Arrangements, Topology, Volume 32, 1993.

Crossrefs

A diagonal of A060637.

Cf. A006245 (two-dimensional tilings), A060595-A060602, A351384.