A275518 -id:A275518 - cp's OEIS frontend

A239911 Erroneous version of A275518.

Original entry on oeis.org

1, 2, 5, 16, 67, 364, 2445, 19296, 173015, 1720924

Offset: 1

N. J. A. Sloane, Apr 09 2014

dead

Sallee, John F. A note on minimal triangulations of an n-cube. Discrete Appl. Math. 4 (1982), no. 3, 211--215. MR0675850 (84g:52019)
Sallee, John F. 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.

Carl W. Lee, Triangulating the d-cube, Annals of the New York Academy of Sciences 440 (1985): 205-211.
Sallee, John F. A triangulation of the n-cube, Discrete Math. 40 (1982), no. 1, 81--86. MR0676714 (84d:05065b)

Cf. A019502, A019503, A019504, A166932.

A019503 Simplexity of the n-cube: minimal cardinality of triangulation of n-cube using n-simplices whose vertices are vertices of the n-cube.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

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.

A019502 Number of simplices in minimal decomposition of an n-cube.

Original entry on oeis.org

1, 2, 5, 16, 67

Offset: 1

N. J. A. Sloane

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.

A352882 a(n) is the number of plane corner cuts of size n.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 7, 8, 10, 12, 13, 16, 16, 18, 20, 23, 24, 26, 26, 30, 32, 35, 34, 38, 38, 42, 44, 46, 47, 54, 52, 54, 52, 56, 60, 66, 67, 68, 66, 72, 72, 80, 74, 82, 84, 87, 86, 90, 88, 96, 96, 102, 96, 104, 104, 115, 114, 116, 110, 118, 114, 124, 122, 126, 134, 140, 135, 134, 132, 146, 144, 156, 144, 150, 152, 158

Offset: 0

Stefano Spezia, Apr 07 2022

nonn

In Bergeron and Mazin, a(n) is the number of triangular partitions of size n.

Alejandro B. Galván, Table of n, a(n) for n = 0..10000
François Bergeron and Mikhail Mazin, Combinatorics of Triangular Partitions, arXiv:2203.15942 [math.CO], (2022). See p. 2.
Sylvie Corteel, Gäel Rémond, Gilles Schaeffer, and Hugh Thomas, The Number of Plane Corner Cuts, Adv. in Appl. Math. 23, no. 1, (1999).
Sergi Elizalde and Alejandro B. Galván, Triangular partitions: enumeration, structure, and generation, arXiv:2312.16353 [math.CO], (2023).
Sergi Elizalde and Alejandro B. Galván, Combinatorial properties of triangular partitions, Proceedings of the 36th Conference on Formal Power Series and Algebraic Combinatorics (Bochum), Séminaire Lotharingien de Combinatoire 91B (2024) Article #68, 12 pp.
Alejandro B. Galván, C++ program.

Cf. A007294, A275518.

See the g.f. at page 2 in Corteel et al.

More terms from Alejandro B. Galván, Dec 29 2023

A239912 Number of simplices is middle-cut slicing of n-cube.

Original entry on oeis.org

1, 2, 5, 16, 67, 324, 1962, 13248, 106181, 931300

Offset: 1

N. J. A. Sloane, Apr 09 2014

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).

Other sequences dealing with different ways to attack this problem. They give further references: A019502, A019503, A019504, A166932, A166932, A275518.

cp's OEIS Frontend

A239911 Erroneous version of A275518.

Views

Author

Keywords

References

Links

Crossrefs

A019503 Simplexity of the n-cube: minimal cardinality of triangulation of n-cube using n-simplices whose vertices are vertices of the n-cube.

Views

Author

Keywords

Comments

References

Links

Crossrefs

A019502 Number of simplices in minimal decomposition of an n-cube.

Views

Author

Keywords

References

Links

Crossrefs

A352882 a(n) is the number of plane corner cuts of size n.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A239912 Number of simplices is middle-cut slicing of n-cube.

Views

Author

Keywords

Links

Crossrefs