Idempotent rank in the endomorphism monoid of a nonuniform partition. (Q2786580)
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scientific article; zbMATH DE number 6541565
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Idempotent rank in the endomorphism monoid of a nonuniform partition. |
scientific article; zbMATH DE number 6541565 |
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15 February 2016
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semigroups of transformations
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partitions
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transformation monoids
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idempotent ranks
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generating sets
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numbers of generators
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0.9431338
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0.9325107
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0.91627127
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0.8984731
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0.8898162
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0.88929135
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0.88575256
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0.8848331
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Idempotent rank in the endomorphism monoid of a nonuniform partition. (English)
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The paper determines the minimal number of generators and the minimal number of idempotent generators for the monoid generated by idempotents of the semigroup that consists of all transformations of a fixed finite set preserving parts of a fixed nonuniform partition of this set. Additionally, all idempotent generating sets of minimal size are classified and enumerated. It is also shown that the minimal number of idempotent generators coincides with the minimal number of (arbitrary) generators unless the partition has exactly two parts of size one and at least one other part.
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