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A327230 Number of non-isomorphic set-systems covering n vertices with at least one endpoint/leaf. 11
0, 1, 3, 14, 198 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A set-system is a finite set of finite nonempty sets. Elements of a set-system are sometimes called edges. A leaf is an edge containing a vertex that does not belong to any other edge, while an endpoint is a vertex belonging to only one edge.
Also covering set-systems with minimum vertex-degree 1.
LINKS
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(3) = 14 set-systems:
{{1}} {{1,2}} {{1,2,3}}
{{1},{2}} {{1},{2,3}}
{{2},{1,2}} {{1},{2},{3}}
{{1,3},{2,3}}
{{3},{1,2,3}}
{{1},{3},{2,3}}
{{2,3},{1,2,3}}
{{2},{1,3},{2,3}}
{{2},{3},{1,2,3}}
{{3},{1,3},{2,3}}
{{1},{2},{3},{2,3}}
{{3},{2,3},{1,2,3}}
{{2},{3},{1,3},{2,3}}
{{2},{3},{2,3},{1,2,3}}
CROSSREFS
Unlabeled covering set-systems are A055621.
The labeled version is A327229.
The non-covering version is A327335 (partial sums).
Sequence in context: A344745 A058388 A362385 * A288555 A288563 A081383
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 01 2019
STATUS
approved

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Last modified September 17 08:52 EDT 2024. Contains 375987 sequences. (Running on oeis4.)