A239912 -id:A239912 - cp's OEIS frontend

1, 2, 5, 16, 67, 308, 1493

Offset: 1

5522 <= a(8) <= 11944 [Haiman, Ziegler]. - Jonathan Vos Post, Jul 13 2005

H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, C9.
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.9, p. 512.
Warren D. Smith, Lower bounds for triangulations of the N-cube, manuscript, 1994.
Gunter M. Ziegler, Lectures on Polytopes, Revised First Edn., Graduate Texts in Mathematics, Springer, 1994, p. 147.

A. Glazyrin, Lower bounds for the simplexity of the n-cube, Discrete Math. 312 (2012), no. 24, 3656--3662. MR2979495. - _N. J. A. Sloane_, Nov 07 2012
R. B. Hughes and M. R. Anderson, Simplexity of the cube, Discrete Mathematics, 158 (1996) 99-150, esp. p. 100.
Mark Haiman, A simple and relatively efficient triangulation of the n-cube, Discrete Comput. Geometry 6 (1991), 287-289.
D. Orden and F. Santos, Asymptotically efficient triangulations of the d-cube, Discr. Comput. Geom. 30 (2003) 509, Table 1.
Warren D. Smith, A lower bound for the simplexity of the n-cube via hyperbolic volumes, Combinatorics of polytopes, European J. Combin. 21 (2000), no. 1, 131-137. MR1737333 (2001c:52004).
Chuanming Zong, What is known about unit cubes, Bull. Amer. Math. Soc., 42 (2005), 181-211.

Other sequences dealing with different ways to attack this problem. They give further references: A019502, A019504, A166932, A166932, A239912, A275518.

1, 2, 5, 16, 67

Offset: 1

H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, Section C9.
R. K. Guy, What is the simplexity of the d-cube?, Amer. Math. Monthly, 91:10 (1984), 628-629.

A. Bliss, F. E. Su, Lower bounds for simplicial covers and triangulations of cubes, arXiv:math/0310142 [math.CO], 2003 (see Table 1 page 4).
A. Bliss, F. E. Su. Lower bounds for simplicial covers and triangulations of cubes, Discrete Comput. Geom. 33 (2005), 669-686.
R. B. Hughes and M. R. Anderson, Simplexity of the cube, Discrete Math., 158(1-3):99-150, 1996.
John F. Sallee, A note on minimal triangulations of an n-cube, Discrete Appl. Math. 4 (1982), no. 3, 211--215. MR0675850 (84g:52019).
John F. Sallee, The middle-cut triangulations of the n-cube, SIAM J. Algebraic Discrete Methods 5 (1984), no. 3, 407--419. MR0752044 (86c:05054). See Table 2.
John F. Sallee, A triangulation of the n-cube, Discrete Math. 40 (1982), no. 1, 81--86. MR0676714 (84d:05065b).

Other sequences dealing with different ways to attack this problem. They give further references: A019503, A019504, A166932, A166932, A239912, A275518.

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