A192102 Number of distinct (unordered) pairs of partitions of a 9-element set that have Rand distance n.

31572, 141624, 452508, 1341648, 3266172, 7234374, 12259368, 18992502, 23324140, 28129626, 26605908, 26190612, 21568932, 17119818, 13040280, 8948079, 6244308, 3679032, 2431044, 1250109, 640908, 315828, 197568, 57288, 46116, 30366, 25732, 7695, 4104, 2226, 3780, 2205, 1344, 378, 36, 1

Offset: 1

Author

Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Aug 08 2011

Keywords

• nonn
• fini
• full

Comments

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.

Links

• F. Ruskey and J. Woodcock, The Rand and block distances of pairs of set partitions, Combinatorial algorithms, 287-299, Lecture Notes in Comput. Sci., 7056, Springer, Heidelberg, 2011.

Crossrefs

Cf. A192100 for set sizes 2..7. A192098 for set size 8.