A007815 Number of triangulations of cyclic 3-polytope C(3,n+3).

1, 2, 6, 25, 138, 972, 8477, 89405, 1119280, 16384508, 276961252, 5349351298, 116985744912, 2873993336097, 78768494976617

Offset

1,2

Comments

a(n) is also the number of persistent graphs on n+1 vertices. - Malte Renken, Jun 30 2020

References

J. Rambau and F. Santos, The Baues problem for cyclic polytopes I, In "Special issue on Combinatorics of convex polytopes" (K. Fukuda and G. M. Ziegler, eds.), European J. Combin. 21:1 (2000), 65-83.

TOPCOM: Triangulations of Point Configurations and Oriented Matroids (ZIB Report 02-17). Proceedings of the International Congress of Mathematical Software ICMS 2002.

Links

Table of n, a(n) for n=1..15.

C. A. Athanasiadis, J. A. De Loera, V. Reiner and F. Santos, Fiber polytopes for the projections between cyclic polytopes, European Journal of Combinatorics, Volume: 21, Issue: 1, 2000, pp. 19 - 47.

M. Azaola and F. Santos, The number of triangulations of the cyclic polytope C(n,n-4), Discrete Comput. Geom., 27 (2002), 29-48.

Vincent Froese, Malte Renken, Persistent Graphs and Cyclic Polytope Triangulations, arXiv:1911.05012 [cs.DM], 2020. See Table 1.

Michael Joswig, Lars Kastner, New counts for the number of triangulations of cyclic polytopes, arXiv:1804.08029 [math.CO], 2018. See Table 1 p. 7.

J. Rambau, TOPCOM

Prog

(TOPCOM) cyclic 14 3 | points2ntriangs -v

Crossrefs

Cf. A028441.

Sequence in context: A255841 A197772 A135881 * A195259 A292748 A178087

Adjacent sequences: A007812 A007813 A007814 * A007816 A007817 A007818

Keyword

hard,nonn

Author

reiner(AT)math.umn.edu (Victor Reiner), edelman(AT)math.umn.edu (Paul Edelman)

Extensions

a(8) and a(9) computed by J. Rambau.

a(7) corrected and a(10) computed by Jörg Rambau, Sep 19 2006, using the TOPCOM software.

Typo in a(8) fixed and a(11) computed using the TOPCOM software by Jörg Rambau, Aug 11 2011

a(12) (computed by Joswig & Kastner) from Michel Marcus, Apr 23 2018

a(13) to a(15) (computed by Froese & Renken) from Malte Renken, Jun 30 2020

Status

approved