Some Remarks on the Combinatorics of ISn
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\noindent 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 the ratio |ISn|/|End(ISn)| is asymptotically 0, answering a question 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.
KeywordsAsymptotic Behavior Combinatorial Property Nilpotent Element Endomorphism Semigroup
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