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%I #39 Nov 17 2017 05:47:50
%S 1,2,5,16,67,308,1493
%N Simplexity of the n-cube: minimal cardinality of triangulation of n-cube using n-simplices whose vertices are vertices of the n-cube.
%C 5522 <= a(8) <= 11944 [Haiman, Ziegler]. - _Jonathan Vos Post_, Jul 13 2005
%D H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, C9.
%D Warren D. Smith, Lower bounds for triangulations of the N-cube, manuscript, 1994.
%D Gunter M. Ziegler, Lectures on Polytopes, Revised First Edn., Graduate Texts in Mathematics, Springer, 1994, p. 147.
%H A. Glazyrin, <a href="http://dx.doi.org/10.1016/j.disc.2012.09.002">Lower bounds for the simplexity of the n-cube</a>, Discrete Math. 312 (2012), no. 24, 3656--3662. MR2979495. - From N. J. A. Sloane, Nov 07 2012
%H R. B. Hughes and M. R. Anderson, <a href="http://dx.doi.org/10.1016/0012-365X(95)00075-8">Simplexity of the cube</a>, Discrete Mathematics, 158 (1996) 99-150, esp. p. 100.
%H Mark Haiman, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN000364819">A simple and relatively efficient triangulation of the n-cube</a>, Discrete Comput. Geometry 6 (1991), 287-289.
%H D. Orden, F. Santos, <a href="http://dx.doi.org/10.1007/s00454-003-2845-5">Asymptotically efficient triangulations of the d-cube</a>, Discr. Comput. Geom. 30 (2003) 509, Table 1.
%H Warren D. Smith, <a href="http://dx.doi.org/10.1006/eujc.1999.0327">A lower bound for the simplexity of the n-cube via hyperbolic volumes, Combinatorics of polytopes</a>. European J. Combin. 21 (2000), no. 1, 131-137. MR1737333 (2001c:52004).
%H Chuanming Zong, <a href="http://dx.doi.org/10.1090/S0273-0979-05-01050-5">What is known about unit cubes</a>, Bull. Amer. Math. Soc., 42 (2005), 181-211.
%Y Other sequences dealing with different ways to attack this problem. They give further references: A019502, A019504, A166932, A166932, A239912, A275518.
%K nonn,hard,nice,more
%O 1,2
%A _N. J. A. Sloane_
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