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Number of distinct (unordered) pairs of partitions of a 10-element set that have Rand distance n.
1

%I #18 Oct 07 2013 01:11:45

%S 186300,887220,3060360,9883440,26969040,67288830,141778440,256463820,

%T 399874640,547907454,670419540,742419510,744780330,701747010,

%U 607809750,520591950,377521875,312082260,198307620,158606532,87210930,63688410,33243120,25703205,11343906,6764940,3272500,2003805,1532340,757080,211410,212625,198345,138600,82512,21080,16200,15750,14910,13545,7245,3270,630,45,1

%N Number of distinct (unordered) pairs of partitions of a 10-element set that have Rand distance n.

%C The Rand distance of a pair of set partitions is the number of unordered pairs {x; y} such that there is a block in one partition containing both x and y, but x and y are in different blocks in the other partition.

%H F. Ruskey and J. Woodcock, <a href="http://webhome.cs.uvic.ca/~ruskey/Publications/RandDist/RandDist.html">The Rand and block distances of pairs of set partitions</a>, Combinatorial algorithms, 287-299, Lecture Notes in Comput. Sci., 7056, Springer, Heidelberg, 2011.

%Y Cf. A192100 for set sizes 2..7. A192098 and A192102 for set sizes 8 and 9.

%K nonn,fini,full

%O 1,1

%A _Frank Ruskey_ and Yuji Yamauchi (eugene.uti(AT)gmail.com), Aug 08 2011