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A129907 Greatest prime factor of the number of subsets S of the power set P{1,2,...,n} such that: {1}, {2},..., {n} are all elements of S; if X and Y are elements of S and X and Y have a nonempty intersection, then the union of X and Y is an element of S. 0
2, 3, 7, 683, 143328791 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

The references are about the notion of connectivity spaces (in French, "espaces connectifs"): the sets S are the finite connectivity structures. For example, the set {1, 2, 3} in the above example is the Borromean structure. The computation of a(6) is entirely based on the work of Wim van Dam (cf. A072446).

REFERENCES

R. Borger, Connectivity spaces and component categories, Categorical topology, International Conference on Categorical Topology, Berlin, Heldermann, 1984.

G. Matheron and J. Serra, Strong filters and connectivity, in Image Analysis and Mathematical Morphology 2, London, Academic Press, 1988, pp. 141-157.

LINKS

Table of n, a(n) for n=2..6.

Wim van Dam, SubPower Set Sequences.

S. Dugowson, Les frontieres dialectiques, Mathematiques et sciences humaines, no. 177, Spring 2007.

S. Dugowson, Representation of finite connective spaces, arXiv:0707.2542 [math.GN], 2007.

EXAMPLE

a(3)=3 because of the 12=3*2^2 subsets: {{1}, {2}, {3}}; {{1}, {2}, {3}, {1, 2}}; {{1}, {2}, {3}, {1, 3}}; {{1}, {2}, {3}, {2, 3}}; {{1}, {2}, {3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {2, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {2, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}.

CROSSREFS

Cf. A072446.

Sequence in context: A334726 A062615 A180162 * A046284 A069503 A077524

Adjacent sequences:  A129904 A129905 A129906 * A129908 A129909 A129910

KEYWORD

more,nonn,uned

AUTHOR

S. Dugowson (dugowson(AT)ext.jussieu.fr), Jun 08 2007

STATUS

approved

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Last modified June 21 14:56 EDT 2021. Contains 345364 sequences. (Running on oeis4.)