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Idempotent rank in the endomorphism monoid of a non-uniform partition

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Date
02/2016
Author
Dolinka, Igor
East, James
Mitchell, James D.
Keywords
Transformation semigroups
Idempotents
Generators
Rank
Idempotent rank
QA Mathematics
T-NDAS
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Abstract
We calculate the rank and idempotent rank of the semigroup E(X,P) generated by the idempotents of the semigroup T(X,P), which consists of all transformations of the finite set X preserving a non-uniform partition P. We also classify and enumerate the idempotent generating sets of this minimal possible size. This extends results of the first two authors in the uniform case.
Citation
Dolinka , I , East , J & Mitchell , J D 2016 , ' Idempotent rank in the endomorphism monoid of a non-uniform partition ' , Bulletin of the Australian Mathematical Society , vol. 93 , no. 1 , pp. 73-91 . https://doi.org/10.1017/S0004972715000751
Publication
Bulletin of the Australian Mathematical Society
Status
Peer reviewed
DOI
https://doi.org/10.1017/S0004972715000751
ISSN
0004-9727
Type
Journal article
Rights
© 2016, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at journals.cambridge.org / https://dx.doi.org/10.1017/S0004972715000751
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/9275

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