Idempotent rank in finite full transformation semigroups
1990 ◽
Vol 114
(3-4)
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pp. 161-167
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Keyword(s):
SynopsisThe subsemigroup Singn of singular elements of the full transformation semigroup on a finite set is generated by n(n − l)/2 idempotents of defect one. In this paper we extend this result to the subsemigroup K(n, r) consisting of all elements of rank r or less. We prove that the idempotent rank, defined as the cardinality of a minimal generating set of idempotents, of K(n, r) is S(n, r), the Stirling number of the second kind.
2015 ◽
Vol 25
(08)
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pp. 1187-1222
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2012 ◽
Vol 05
(03)
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pp. 1250035
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1988 ◽
Vol 30
(2)
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pp. 203-211
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1992 ◽
Vol 120
(1-2)
◽
pp. 129-142
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1990 ◽
Vol 115
(3-4)
◽
pp. 289-299
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1990 ◽
Vol 116
(3-4)
◽
pp. 359-366
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2005 ◽
Vol 71
(1)
◽
pp. 69-74
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1982 ◽
Vol 23
(2)
◽
pp. 137-149
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2016 ◽
Vol 16
(07)
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pp. 1750138
Keyword(s):