2,1

The references are about the notion of connectivity spaces (in French, "espaces connectifs") : the sets S are the finite connectivity structures. Fo 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).

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

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

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

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

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}}.

Cf. A072446.

Adjacent sequences: A129904 A129905 A129906 this_sequence A129908 A129909 A129910

Sequence in context: A100763 A132538 A062615 this_sequence A046284 A069503 A077524

more,nonn,uned

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