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A326939 Number of T_0 sets of subsets of {1..n} that cover all n vertices. 15
2, 2, 8, 192, 63384, 4294003272, 18446743983526539408, 340282366920938462946865774750753349904, 115792089237316195423570985008687907841019819456486779364848020385134373080448 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges).

LINKS

Table of n, a(n) for n=0..8.

FORMULA

a(n) = 2 * A059201(n).

Inverse binomial transform of A326941.

EXAMPLE

The a(0) = 2 through a(2) = 8 sets of subsets:

  {}    {{1}}     {{1},{2}}

  {{}}  {{},{1}}  {{1},{1,2}}

                  {{2},{1,2}}

                  {{},{1},{2}}

                  {{},{1},{1,2}}

                  {{},{2},{1,2}}

                  {{1},{2},{1,2}}

                  {{},{1},{2},{1,2}}

MATHEMATICA

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

Table[Length[Select[Subsets[Subsets[Range[n]]], Union@@#==Range[n]&&UnsameQ@@dual[#]&]], {n, 0, 3}]

CROSSREFS

The non-T_0 version is A000371.

The case without empty edges is A059201.

The non-covering version is A326941.

The unlabeled version is A326942.

The case closed under intersection is A326943.

Cf. A003180, A003181, A003465, A316978, A319564, A319637, A326940, A326947.

Sequence in context: A270316 A069561 A180370 * A011148 A176020 A048650

Adjacent sequences:  A326912 A326913 A326914 * A326940 A326941 A326942

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 07 2019

STATUS

approved

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Last modified September 19 04:39 EDT 2019. Contains 327187 sequences. (Running on oeis4.)