Some remarks on the combinatorics of ISn
نویسندگان
چکیده
We describe the asymptotic behavior of the cardinalities of the finite symmetric inverse semigroup ISn and its endomorphism semigroup. This is applied to show that |ISn|/|End(ISn)| is asymptotically 0, solving a problem of Schein and Teclezghi. We also apply our results to compute the distributions of elements from ISn with respect to certain combinatorial properties, and to compute the generating functions for |ISn| and for the number of nilpotent elements in ISn.
منابع مشابه
Combinatorics and distributions of partial injections
We obtain several combinatorial results about chains, cycles and orbits of the elements of the symmetric inverse semigroup ISn and the set Tn of nilpotent elements in ISn. We also get some estimates for the growth of |ISn| and |Tn|, and study random products of elements from ISn.
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