In combinatorics, the nth Bell number, named after Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it. Starting with B0 = B1 = 1, the first few Bell numbers are:
- 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, … (sequence A000110 in OEIS).
(See also breakdown by number of subsets/equivalence classes.)
Read more about Bell Number: Partitions of A Set, Properties of Bell Numbers, Asymptotic Limit and Bounds, Triangle Scheme For Calculating Bell Numbers, Prime Bell Numbers
Famous quotes containing the words bell and/or number:
“There is evidence that all too many people are approaching parenthood with a dangerous lack of knowledge and skill. The result is that many children are losing out on what ought to be an undeniable right—the right to have parents who know how to be good parents, parents skilled in the art of “parenting.””
—T. H. Bell (20th century)
“As Jerome expanded, its chances for the title, “the toughest little town in the West,” increased and when it was incorporated in 1899 the citizens were able to support the claim by pointing to the number of thick stone shutters on the fronts of all saloons, gambling halls, and other places of business for protection against gunfire.”
—Administration in the State of Ariz, U.S. public relief program (1935-1943)