A105232 -id:A105232 - cp's OEIS frontend

A350808 Erroneous version of A105232.

1, 2, 8, 172

Offset: 1

N. J. A. Sloane, Jan 17 2022

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Included in accordance with OEIS policy of including published but erroneous sequences to serve as pointers to the correct values.

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

A105231 Number of n-dimensional polytopes with vertices from {0,1}^n up to (0,1)-equivalence.

Original entry on oeis.org

1, 2, 12, 347, 1226525, 400507800465455

Offset: 1

N. J. A. Sloane, Apr 16 2005

a(6) = 400507800465455 is obtained as the sum of the number of 6-dimensional polytopes with up to 12 vertices, 94826705, given in the footnote in p. 119 of Aichholzer (2000), and the counts for k > 12 vertices F_6(k) given in tables 3, 6 and 7 of Chen & Guo (2014). Chen & Guo have typos: F_5(29) in table 2 should be 10 and F_5(16) in table 5 should be 169110 (cf. polyDB or Aichholzer's table 2). - Andrey Zabolotskiy, Jun 20 2023

Oswin Aichholzer, Extremal Properties of 0/1-Polytopes of Dimension 5. In: Polytopes - Combinatorics and Computation, DMV Seminar vol 29, Birkhäuser, Basel, 2000.
William Y. C. Chen and Peter L. Guo, Equivalence Classes of Full-Dimensional 0/1-Polytopes with Many Vertices, Discrete Comput. Geom., 52 (2014), 630-662.
Andreas Paffenholz and the polymake team, polyDB. See Polytopes > Geometric Polytopes > 0/1 Polytopes by Oswin Aichholzer.
Chuanming Zong, What is known about unit cubes, Bull. Amer. Math. Soc., 42 (2005), 181-211.

Cf. A105230, A105232.

a(6) from Andrey Zabolotskiy, Jun 20 2023

A105230 Number of n-dimensional polytopes with vertices from {0,1}^n.

Original entry on oeis.org

1, 5, 151, 60879, 4292660729, 18446743888401503325

Offset: 1

N. J. A. Sloane, Apr 16 2005

Rado Rakotonarivo, Sur la combinatoire des polytopes en nombres entiers, génération aléatoire et énumération, Thèse de doctorat en Informatique, Université Sorbonne Paris Nord, 2020.
Chuanming Zong, What is known about unit cubes, Bull. Amer. Math. Soc., 42 (2005), 181-211.

Cf. A105231, A105232.

a(6) from Rakotonarivo added by Andrey Zabolotskiy, Jun 19 2023

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A350808 Erroneous version of A105232.

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A105231 Number of n-dimensional polytopes with vertices from {0,1}^n up to (0,1)-equivalence.

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A105230 Number of n-dimensional polytopes with vertices from {0,1}^n.

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