This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060601 #31 Mar 10 2023 11:04:07
%S A060601 1,2,22,16360,613773463394
%N A060601 Number of tilings of the 9-dimensional zonotope constructed from D vectors.
%C A060601 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 d=9 and D varies.
%C A060601 Also the number of signotopes of rank 10. A signotope 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). - _Manfred Scheucher_, Feb 09 2022
%D A060601 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.
%D A060601 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.
%H A060601 Helena Bergold, Stefan Felsner, and Manfred Scheucher, <a href="http://page.math.tu-berlin.de/~scheuch/publ/bfs-ehds-eurocg22.pdf">Extendability of higher dimensional signotopes</a>, Proc. 38th Eur. Wksp. Comp. Geom. (EuroCG), 2022. See also <a href="https://arxiv.org/abs/2303.04079">arXiv:2303.04079</a> [math.CO], 2023.
%H A060601 N. Destainville, R. Mosseri and F. Bailly, <a href="https://arxiv.org/abs/cond-mat/0004145">Fixed-boundary octagonal random tilings: a combinatorial approach</a>, arXiv:cond-mat/0004145 [cond-mat.stat-mech], 2000.
%H A060601 N. Destainville, R. Mosseri and F. Bailly, <a href="https://doi.org/10.1023/A:1026564710037">Fixed-boundary octagonal random tilings: a combinatorial approach</a>, Journal of Statistical Physics, 102 (2001), no. 1-2, 147-190.
%H A060601 S. Felsner and H. Weil, <a href="http://doi.org/10.1016/S0166-218X(00)00232-8">Sweeps, arrangements and signotopes</a>, Discrete Applied Mathematics, Volume 109, Issues 1-2, 2001, Pages 67-94.
%H A060601 M. Latapy, <a href="https://arxiv.org/abs/math/0008022">Generalized Integer Partitions, Tilings of Zonotopes and Lattices</a>, arXiv:math/0008022 [math.CO], 2000.
%H A060601 G. M. Ziegler, <a href="https://www.mi.fu-berlin.de/math/groups/discgeom/ziegler/Preprintfiles/025PREPRINT.pdf">Higher Bruhat Orders and Cyclic Hyperplane Arrangements</a>, Topology, Volume 32, 1993.
%F A060601 Asymptotics: a(n) = 2^(Theta(n^9)). This is Bachmann-Landau notation, that is, there are constants n_0, c, and d, such that for every n >= n_0 the inequality 2^{c n^9} <= a(n) <= 2^{d n^9} is satisfied. - _Manfred Scheucher_, Sep 22 2021
%e A060601 For any d, the only possible tile for Z(d,d) is Z(d,d) itself, therefore the first term of the series is 1. It is well known that there are always two d-tilings of Z(d+1,d), therefore the second term is 2. More examples are available on my web page.
%Y A060601 Cf. A006245 (two-dimensional tilings), A060595-A060602.
%Y A060601 Column k=9 of A060637.
%K A060601 nonn,nice
%O A060601 9,2
%A A060601 Matthieu Latapy (latapy(AT)liafa.jussieu.fr), Apr 12 2001
%E A060601 a(13) from _Manfred Scheucher_, Mar 07 2022
%E A060601 Edited by _Manfred Scheucher_, Mar 08 2022