Counting \(f\) such that \(f \circ g = g \circ f\) (Q678723)
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scientific article; zbMATH DE number 1003984
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counting \(f\) such that \(f \circ g = g \circ f\) |
scientific article; zbMATH DE number 1003984 |
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Counting \(f\) such that \(f \circ g = g \circ f\) (English)
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25 June 1997
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Let \(A\) be a finite set and let \(g\) be a given mapping, \(g:A\to A.\) An algorithm for finding all \(f:A\to A\) such that \(f\circ g=g\circ f\) is described. The combinatorial and algebraic results are already known, see references of \textit{M. Novotný} [Arch. Math., Brno 26, No. 2/3, 155-164 (1990; Zbl 0741.08001)]. The algorithms quoted above is applied to find explicit formulae for the number of all infra-endomorphisms of the finite cyclic groups as well as that of the finite dihedral groups.
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finite set
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mapping
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algorithm
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infra-endomorphisms
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