A329980
a(n) is the number of non-isomorphic generalized signotopes on n elements (cf. A328377) w.r.t. relabeling of the vertices.
Original entry on oeis.org
1, 2, 6, 167, 63451
Offset: 3
- H. Bergold, S. Felsner, M. Scheucher, F. Schröder, and R. Steiner, Topological Drawings meet Classical Theorems from Convex Geometry, in preparation.
- M. Balko, R. Fulek, and J. Kynčl, Crossing Numbers and Combinatorial Characterization of Monotone Drawings of K_n, Discrete & Computational Geometry, Volume 53, Issue 1, 2015, Pages 107-143.
- S. Felsner and H. Weil, Sweeps, arrangements and signotopes, Discrete Applied Mathematics, Volume 109, Issues 1-2, 2001, Pages 67-94.
A060600
Number of tilings of the 8-dimensional zonotope constructed from D vectors.
Original entry on oeis.org
1, 2, 20, 7658, 12954016496, 10592917773063552232751878
Offset: 8
Matthieu Latapy (latapy(AT)liafa.jussieu.fr), Apr 12 2001
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.
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- 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.
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- 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.
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- 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.
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