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Bell numbers: Difference between revisions

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Bell numbers (view source)

Revision as of 18:11, 22 July 2021

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