

A028497


Maximum number of facets of ndimensional polytope with {0,1}coordinates.


0




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

U. Kortenkamp, J. RichterGebert, Aravamuthan Sarangarajan and G. M. Ziegler, Extremal properties of 0/1polytopes, Discrete and Computational Geometry 17 (issue 4) (1997), 439448.


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 0/1polytope of dimension 13, with 254 vertices and at least 17464356 facets.  Jonathan Vos Post, Jul 13 2005


CROSSREFS



KEYWORD

nonn,hard,nice,more


AUTHOR

Ulrich Kortenkamp (kortenka(AT)inf.fuberlin.de), Oswin Aichholzer (oaich(AT)igi.tugraz.ac.at)


STATUS

approved



