| Title | Largest 2-generated subsemigroups of the symmetric inverse semigroup |
| Publication Type | Unpublished |
| Year of Publication | 2006 |
| Authors | André JM, Fernandes VH, Mitchell JD |
| Series Title | Preprint |
| Abstract | The symmetric inverse monoid In is the set of all partial permutations of an n-element set. The largest possible size of a 2-generated subsemigroup of In is determined. Examples of semigroups with these sizes are given. Consequently, if M(n) denotes this maximum, it is shown that M(n)/|In| → 1 as n → ∞. Furthermore, we may deduce, the already known fact, that In embeds as a local submonoid of an inverse 2-generated subsemigroup of In+1. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2006/11_06.pdf |