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%I #19 Apr 01 2014 10:29:29
%S 1,3,9,11,15,129,131,137,139,143,153,171,175,255
%N Encoding of topologies generated by classes of sets.
%C We map {}, a, b, c, d, ... to 1, 2, 4, 16, 256, ..., i.e., to 2^0, 2^1, 2^2, 2^4, 2^8, ... . Sets with more than 1 element are mapped to the product. So ab (a shorthand notation for {a,b}) is mapped to 2^1 * 2^2 = 2^3. The topology is represented by the sum of the representations of its components.
%C The sequence encodes unlabeled topologies as described in A000798.
%e 1+2+8 = 11 (binary 1011) encodes {}, a, ab, which is the least encoding of this topology, so 11 is in the sequence.
%e 1+4+8 = 13 (binary 1101) encodes {}, b, ab which is topologically equivalent and larger, so it is not in the sequence. The number of equivalent cases corresponding to a(n) begins 1; 1,1,2; 1,1,3,3,6,3,3,3,6; ... and is counted by A001928 (labeled topologies).
%e 171 (binary 1011011) is in the sequence because we map {}, a, ab, ac, abc to 1 + 2 + 8 + 32 + 128.
%Y Cf. A000798, A001928.
%K more,nonn,base
%O 0,2
%A _Alford Arnold_, Sep 26 2002
%E Edited by _Franklin T. Adams-Watters_, Mar 29 2014
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