A261005 Number of unlabeled simplicial complexes with n nodes.

1, 1, 2, 5, 20, 180, 16143, 489996795, 1392195548399980210, 789204635842035039135545297410259322

Offset: 0

Author

N. J. A. Sloane, Aug 13 2015

Keywords

• nonn

Comments

Also the number of non-isomorphic antichains of nonempty sets covering n vertices. The labeled case is A006126, except with a(0) = 1. - Gus Wiseman, Feb 23 2019

Examples

			From _Gus Wiseman_, Feb 23 2019: (Start)
Non-isomorphic representatives of the a(0) = 1 through a(4) = 20 antichains:
  {}  {{1}}  {{12}}    {{123}}         {{1234}}
             {{1}{2}}  {{1}{23}}       {{1}{234}}
                       {{13}{23}}      {{12}{34}}
                       {{1}{2}{3}}     {{14}{234}}
                       {{12}{13}{23}}  {{1}{2}{34}}
                                       {{134}{234}}
                                       {{1}{24}{34}}
                                       {{1}{2}{3}{4}}
                                       {{13}{24}{34}}
                                       {{14}{24}{34}}
                                       {{13}{14}{234}}
                                       {{12}{134}{234}}
                                       {{1}{23}{24}{34}}
                                       {{124}{134}{234}}
                                       {{12}{13}{24}{34}}
                                       {{14}{23}{24}{34}}
                                       {{12}{13}{14}{234}}
                                       {{123}{124}{134}{234}}
                                       {{13}{14}{23}{24}{34}}
                                       {{12}{13}{14}{23}{24}{34}}
(End)
		

References

• Benoît Jubin, Posting to Sequence Fans Mailing List, Aug 12 2015.

Links

• C. Lienkaemper, A. Shiu, and Z. Woodstock, Obstructions to convexity in neural codes, Preprint 2015.
• Francisco Ponce Carrión and Seth Sullivant, Marginal Independence and Partial Set Partitions, arXiv:2402.16292 [math.ST], 2024. See p. 21.
• Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Crossrefs

Apart from a(0), same as A006602, and after subtracting 1, A007411.

Cf. A000372, A003182, A006126, A014466, A261006, A304997, A304998, A306505, A306550, A321679.

Formula

First differences of A306505. - Gus Wiseman, Feb 23 2019

a(n) = A003182(n) - A003182(n-1) for n > 0. - Andrew Howroyd, May 28 2023

Extensions

a(8)-a(9) added using A003182 by Andrew Howroyd, May 28 2023