Infinite partition monoids. (Q2876611)
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scientific article; zbMATH DE number 6332010
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Infinite partition monoids. |
scientific article; zbMATH DE number 6332010 |
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19 August 2014
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partition monoids
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generators
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invertible elements
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idempotents
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symmetric groups
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0.8855752
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0.88530815
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0.86355805
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0.86104673
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0.86056185
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0.85874563
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Infinite partition monoids. (English)
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The paper studies generation properties for partition monoids on arbitrary sets. The main result asserts that the partition monoid can be generated by its group of invertible elements with at least two additional partitions and all pairs of such partitions are classified. There is also a classification of all pairs of partitions which, together with all idempotents, generate the partition monoid. There are also some bonus results, in particular, it is shown that any countable subset of the partition monoid is contained in a 4-generated subsemigroup, and that the length function on the partition monoid is bounded for any generating set.
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