In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy, they are named after Eric Temple Bell, who wrote about them in the 1930s.
The Bell numbers are denoted , where is an integer greater than or equal to zero. Starting with , the first few Bell numbers are
(sequence A000110 in the OEIS).
The Bell number counts the different ways to partition a set that has exactly elements, or equivalently, the equivalence relations on it. also counts the different rhyme schemes for -line poems.[1]
As well as appearing in counting problems, these numbers have a different interpretation, as moments of probability distributions. In particular, is the -th moment of a Poisson distribution with mean 1.
1,2,5,15,52,203,877,4140,\dots } (sequence A000110 in the OEIS). The Bellnumber B n {\displaystyle B_{n}} counts the different ways to partition a set...
In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the weak orderings on a set of n {\displaystyle n} elements...
Motzkin number, a Bellnumber, and the third (or fourth) Fibonacci number. 2 is a meandric number, a semi-meandric number, and an open meandric number. 2 {\displaystyle...
k is the total number of partitions of a set with n members. This number is known as the nth Bellnumber. Analogously, the ordered Bell numbers can be...
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in various genres, Bell has 18 US top 10 hits to his credit, including eight number ones, all since 2018. Billboard called Bell's impact on the top of...
Cn is the number of noncrossing partitions of the set {1, ..., n}. A fortiori, Cn never exceeds the n-th Bellnumber. Cn is also the number of noncrossing...
1974 – Number 97 US Atlantic Records "Hazell" – 1978 – Number 37 UK – Swan Song Records "Hold Me" – 1981 – B. A. Robertson and Maggie Bell – Number 11 UK...
by the Bell. The series premiered on August 20, 1989, and ended on May 22, 1993, with 86 episodes produced spanning four seasons. The number of episodes...
mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling and Bell numbers....
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The Bell 214ST is a medium-lift, twin-engine helicopter descended from Bell Helicopter's ubiquitous UH-1 Huey series. Though it shares a type number with...
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