Theoretica chimica acta

, Volume 67, Issue 6, pp 427–437 | Cite as

On the interrelation between orbits and double cosets

  • Werner Hässelbarth


Orbits and double cosets are intimately related: double cosets can always be looked upon as being orbits and often orbits can be identified with double cosets, in reverse. This note presents two such situations where orbits can be traced back to double cosets: the restriction of transitive permutation representations to subgroups and the cartesian product of two transitive permutation representations. These results readily apply to standard topics in chemical combinatorics dealing with isomers and isomerizations but equally like to less familiar combinatorial schemes such as Redfield's.

Key words

Enumeration under group action orbits double cosets permutational isomerism 


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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Werner Hässelbarth
    • 1
  1. 1.Institut für QuantenchemieFreie Universität BerlinBerlin 45Germany

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