Counting Partitions
The total number of partitions of an n-element set is the Bell number Bn. The first several Bell numbers are B0 = 1, B1 = 1, B2 = 2, B3 = 5, B4 = 15, B5 = 52, and B6 = 203. Bell numbers satisfy the recursion
and have the exponential generating function
The number of partitions of an n-element set into exactly k nonempty parts is the Stirling number of the second kind S(n, k).
The number of noncrossing partitions of an n-element set is the Catalan number Cn, given by
Read more about this topic: Partition Of A Set
Famous quotes containing the words counting and/or partitions:
“What culture lacks is the taste for anonymous, innumerable germination. Culture is smitten with counting and measuring; it feels out of place and uncomfortable with the innumerable; its efforts tend, on the contrary, to limit the numbers in all domains; it tries to count on its fingers.”
—Jean Dubuffet (1901–1985)
“Walls have cracks and partitions ears.”
—Chinese proverb.