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Combinatorics and distributions of partial injections

Olexandr Ganyushkin·Volodymyr Mazorchuk
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Abstract

We obtain several combinatorial results about chains, cycles and orbits of the elements of the symmetric inverse semigroup $\IS_n$ and the set $T_n$ of nilpotent elements in $\IS_n$. We also get some estimates for the growth of $|\IS_n|$ and $|T_n|$, and study random products of elements from $\IS_n$.

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Olexandr Ganyushkin, Volodymyr Mazorchuk. 2005-11-17. Combinatorics and distributions of partial injections. https://arxiv.org/abs/math/0511431

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