login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327052 Number of T_0 (costrict) set-systems covering a subset of {1..n} where every two covered vertices appear together in some edge (cointersecting). 8
1, 2, 6, 75, 24981 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A set-system is a finite set of finite nonempty sets. Its elements are sometimes called edges. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. This sequence counts set-systems whose dual is strict and pairwise intersecting.

LINKS

Table of n, a(n) for n=0..4.

FORMULA

Binomial transform of A327053.

EXAMPLE

The a(0) = 1 through a(2) = 6 set-systems:

{} {} {}

{{1}} {{1}}

{{2}}

{{1},{1,2}}

{{2},{1,2}}

{{1},{2},{1,2}}

MATHEMATICA

dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}];

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];

Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], UnsameQ@@dual[#]&&stableQ[dual[#], Intersection[#1, #2]=={}&]&]], {n, 0, 3}]

CROSSREFS

The unlabeled multiset partition version is A319760.

The non-T_0 version is A327039.

The covering case is A327053.

Cf. A051185, A319752, A319774, A327038, A327040.

Sequence in context: A065410 A000721 A262279 * A231508 A136306 A274825

Adjacent sequences: A327049 A327050 A327051 * A327053 A327054 A327055

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 18 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 30 16:07 EST 2023. Contains 359945 sequences. (Running on oeis4.)