A028497 Maximum number of facets of n-dimensional polytope with {0,1}-coordinates.

2, 4, 8, 16, 40

Offset

1,1

Comments

Next term may be 121.

References

Gunter M. Ziegler, Lectures on Polytopes, Revised First Edn., Graduate Texts in Mathematics, Springer, 1994, p. 26.

Links

Table of n, a(n) for n=1..5.

Komei Fukuda , Frequently Asked Questions in Polyhedral Computation

Michael Joswig, polymake Miscellanea

U. Kortenkamp, J. Richter-Gebert, Aravamuthan Sarangarajan and G. M. Ziegler, Extremal properties of 0/1-polytopes, Discrete and Computational Geometry 17 (issue 4) (1997), 439-448.

Ulrich H. Kortenkamp, Current records [archived link]

G. Ziegler, Lectures on 0/1-polytopes, arXiv:math/9909177 [math.CO], 1999.

Chuanming Zong, What is known about unit cubes, Bull. Amer. Math. Soc., 42 (2005), 181-211.

Formula

Asymptotically, the best known bounds are (3.6)^n < a(n) <= (6.4 n!)/(n^1/2) for all sufficiently large n. The parameter 3.6 was determined in March 1997 by Thomas Christhof for a random 0/1-polytope of dimension 13, with 254 vertices and at least 17464356 facets. - Jonathan Vos Post, Jul 13 2005

Crossrefs

Sequence in context: A337673 A162428 A344491 * A197244 A350495 A337581

Adjacent sequences: A028494 A028495 A028496 * A028498 A028499 A028500

Keyword

nonn,hard,nice,more

Author

Ulrich Kortenkamp (kortenka(AT)inf.fu-berlin.de), Oswin Aichholzer (oaich(AT)igi.tu-graz.ac.at)

Status

approved