Largest 2-generated Subsemigroups of the Symmetric Inverse Semigroup
نویسندگان
چکیده
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. AMS 2000 Mathematics subject classification: Primary 20M20 Secondary 20M18
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