A135452 - OEIS

%I #2 Mar 31 2012 20:24:53

%S 1,1,2,3,6,10,20,33,71,117,242,421,877,1468

%N Number of different multisets of differences between ends of n non-intersecting chords joining 2n labeled points around a circle.

%C Represent a set of chords as a collection of pairs of integers. For example, if n=3, one possible connectivity is {{1,4},{2,3},{5,6}}.

%C Define the D-set of a connectivity to be the multiset of differences between connected pairs. In the above example the D-set is {1,1,3}. Since the numbers are on a circle, we can take two possible differences. We take the smaller of the two. Hence the maximal difference can be at most n or n-1 depending on whether n is odd or even. Is another example: the D-set of {{1,6},{2,3},{4,5}} is {1,1,1}.

%C Then the sequence gives the number of distinct D-sets of all possible connectivities.

%C While it is true that if two connectivities have different D-sets they are inequivalent, the converse is not true. consider n=6: Both {{4, 5}, {6, 11}, {2, 3}, {8, 9}, {7, 10}, {1, 12}} and {{4, 5}, {1, 6}, {2, 3}, {8, 9}, {7, 10}, {11, 12}} have the same D-set, namely {1,1,1,1,3,5} but they are inequivalent.

%Y Cf. A001008, A054357.

%K more,nonn

%O 1,3

%A _Arvind Ayyer_, Dec 14 2007, definition corrected Jan 04 2007, Jan 07 2007