Abstract
For given integerm>1, each step-cycle corresponds to a set of permutations such that the step-cycles constitute a set of equivalence classes on the set of all permutations onm elements.
The algorithm has been used in connection with computations to search for groups consisting of a union of disjoint sets of permutations such that each set of permutations corresponds to a step-cycle, see [2] and [8].
Zusammenfassung
Für eine gegebene ganze Zahlm>1 gibt es zu jeder „step-cycle” eine Menge von Permutationen so daß die „step-cycle” eine Menge von Äquivalenzklassen auf der Menge aller Permutationen vonm Elemente bilden. Der Algorithmus ist in Verbindung mit Berechnungen verwendet worden, um Gruppen darzustellen, die von einer Summe elementfremder Mengen von Permutationen bestehen, so daß jede Menge von Permutationen einer „step-cycle” entspricht.
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References
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Mossige, S. Algorithm 19 step-cycle generation. Computing 12, 269–272 (1974). https://doi.org/10.1007/BF02293110
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DOI: https://doi.org/10.1007/BF02293110