Semitransitive subsemigroups of the singular part of the finite symmetric inverse semigroup
Copyright policy )Semitransitive subsemigroups of the singular part of the finite symmetric inverse semigroup
We prove that the minimal cardinality of the semitransitive subsemigroup in the singular part $\IS_n\setminus §_n$ of the symmetric inverse semigroup $\IS_n$ is $2n-p+1$, where $p$ is the greatest proper divisor of $n$, and classify all semitransitive subsemigroups of this minimal cardinality.
- University of Ljubljana Slovenia
- Vrije Universiteit Brussel Belgium
- University of Nova Gorica Slovenia
20M20, minimal cardinality, Group Theory (math.GR), Inverse semigroups, Semigroups of transformations, relations, partitions, etc., semigroups of partial transformations, symmetric inverse semigroup, semitransitivity, FOS: Mathematics, Mathematics - Combinatorics, singular part, Combinatorics (math.CO), symmetric inverse semigroups, Mathematics - Group Theory
20M20, minimal cardinality, Group Theory (math.GR), Inverse semigroups, Semigroups of transformations, relations, partitions, etc., semigroups of partial transformations, symmetric inverse semigroup, semitransitivity, FOS: Mathematics, Mathematics - Combinatorics, singular part, Combinatorics (math.CO), symmetric inverse semigroups, Mathematics - Group Theory
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