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A028497 Maximum number of facets of n-dimensional polytope with {0,1}-coordinates (next term may be 121). 0
2, 4, 8, 16, 40 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

REFERENCES

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.

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

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

LINKS

Author?, Frequently Asked Questions in Polyhedral Computation

Author?, POLYMAKE

Author?, Current records [link is broken]

G. Ziegler, [math/9909177] Lectures on 0/1-polytopes

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 (jvospost3(AT)gmail.com), Jul 13 2005

CROSSREFS

Sequence in context: A095236 A018536 A162428 * A197244 A018575 A013116

Adjacent sequences:  A028494 A028495 A028496 * A028498 A028499 A028500

KEYWORD

nonn,hard,nice

AUTHOR

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

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Last modified February 16 04:18 EST 2012. Contains 205860 sequences.