Bell numbers: Difference between revisions
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;E.G.: |
;E.G.: |
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'''{a b}''' is the same as '''{b a}''', |
: '''{a b}''' is the same as '''{b a}''', and |
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: '''{a} {b}''' is the same as '''{b} {a}'''. |
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;So: |
;So: |
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: '''B<sub>0</sub> = 1''' trivially. There is only one way to partition a set with zero elements: '''{ }''' |
: '''B<sub>0</sub> = 1''' trivially. There is only one way to partition a set with zero elements: '''{ }''' |
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: '''B<sub>1</sub> = 1''' There is only one way to partition a set with one element: '''{a}''' |
: '''B<sub>1</sub> = 1''' There is only one way to partition a set with one element: '''{a}''' |
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: '''B<sub>2</sub> = 2''' Two elements may be partitioned in two ways: '''{a} {b}, {a b}''' |
: '''B<sub>2</sub> = 2''' Two elements may be partitioned in two ways: '''{a} {b}, {a b}''' |
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: '''B<sub>3</sub> = 5''' Three elements may be partitioned in five ways: '''{a} {b} {c}, {a b} {c}, {a} {b c}, {a c} {b}, {a b c}''' |
: '''B<sub>3</sub> = 5''' Three elements may be partitioned in five ways: '''{a} {b} {c}, {a b} {c}, {a} {b c}, {a c} {b}, {a b c}''' |
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: and so on. |
: and so on. |
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;See also: |
;See also: |
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:* '''[[ |
:* '''[[OEIS:A000110|OEIS:A000110 Bell or exponential numbers]]''' |
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:* '''[[ |
:* '''[[OSIS:A011971|OEIS:A011971 Aitken's array]]''' |
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<br><br> |
<br><br> |
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