Abstract
We study the singular part of the partition monoid Pn; that is, the ideal PnSn , where Sn is the symmetric group. Our main results are presentations in terms of generators and relations. We also show that Pn/Sn is idempotent generated, and that its rank and idempotent-rank are both equal to n(n+1)/2. One of our presentations uses an idempotent generating set of this minimal cardinality.
| Original language | English |
|---|---|
| Pages (from-to) | 147-178 |
| Number of pages | 32 |
| Journal | International Journal of Algebra and Computation |
| Volume | 21 |
| Issue number | 45323 |
| DOIs | |
| Publication status | Published - 2011 |