Idempotent rank in the endomorphism monoid of a non-uniform partition
View/ Open
Date
02/2016Keywords
Metadata
Show full item recordAltmetrics Handle Statistics
Altmetrics DOI Statistics
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
ISSN
0004-9727Type
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
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.