cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A305854 Number of unlabeled spanning intersecting set-systems on n vertices.

Original entry on oeis.org

1, 1, 2, 10, 110, 14868, 1289830592
Offset: 0

Views

Author

Gus Wiseman, Jun 11 2018

Keywords

Comments

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge.

Examples

			Non-isomorphic representatives of the a(3) = 10 spanning intersecting set-systems:
  {{1,2,3}}
  {{3},{1,2,3}}
  {{1,3},{2,3}}
  {{2,3},{1,2,3}}
  {{3},{1,3},{2,3}}
  {{3},{2,3},{1,2,3}}
  {{1,2},{1,3},{2,3}}
  {{1,3},{2,3},{1,2,3}}
  {{3},{1,3},{2,3},{1,2,3}}
  {{1,2},{1,3},{2,3},{1,2,3}}

Crossrefs

Cf. A001206, A006126, A051185, A261006, A283877, A304998, A305843, A305844, A305855-A305857.

Formula

a(n) = A305856(n) - A305856(n-1) for n > 0. - Andrew Howroyd, Aug 12 2019

Extensions

a(5) from Andrew Howroyd, Aug 12 2019
a(6) from Bert Dobbelaere, Apr 28 2025

A305857 Number of unlabeled intersecting antichains on up to n vertices.

Original entry on oeis.org

1, 2, 3, 6, 15, 87, 3528, 47174113
Offset: 0

Views

Author

Gus Wiseman, Jun 11 2018

Keywords

Comments

An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other.

Examples

			Non-isomorphic representatives of the a(4) = 15 intersecting antichains:
  {}
  {{1}}
  {{1,2}}
  {{1,2,3}}
  {{1,2,3,4}}
  {{1,3},{2,3}}
  {{1,4},{2,3,4}}
  {{1,3,4},{2,3,4}}
  {{1,2},{1,3},{2,3}}
  {{1,4},{2,4},{3,4}}
  {{1,3},{1,4},{2,3,4}}
  {{1,2},{1,3,4},{2,3,4}}
  {{1,2,4},{1,3,4},{2,3,4}}
  {{1,2},{1,3},{1,4},{2,3,4}}
  {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

Crossrefs

Cf. A001206, A006126, A051185, A261006, A283877, A304998, A305843, A305844, A305854, A305855, A305856.

Formula

a(n) = A305855(0) + A305855(1) + ... + A305855(n). - Brendan McKay, May 11 2020

Extensions

a(6) from Andrew Howroyd, Aug 13 2019
a(7) from Brendan McKay, May 11 2020

A306001 Number of unlabeled intersecting set-systems with no singletons on up to n vertices.

Original entry on oeis.org

1, 1, 2, 8, 84, 13000
Offset: 0

Views

Author

Gus Wiseman, Jun 16 2018

Keywords

Comments

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. A singleton is an edge containing only one vertex.

Examples

			Non-isomorphic representatives of the a(3) = 8 set-systems:
{}
{{1,2}}
{{1,2,3}}
{{1,3},{2,3}}
{{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}

Crossrefs

Cf. A001206, A051185, A048143, A261006, A058891, A261005, A304998, A305854-A305857, A305935, A305999, A306000.

Formula

a(n) = A305856(n) - A000612(n). - Andrew Howroyd, Aug 12 2019

Extensions

a(5) from Andrew Howroyd, Aug 12 2019
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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