'necklace'-type classes of combinatorial compositions

[john n <johnnagelson@yahoo.co.uk>]

Hello, I am a PARI-GP newbie and wondered whether someone might help me with
code for listing the classes of combinatorial compositions of p which
contain q elements, and which are equivalent under reflection or cycling.
These are closely related to "necklaces".

Each equivalence class can be denoted by its lexicographically first
element, e.g. when p=10 and q=3,
{{1,2,6},{2,6,1},{6,1,2},{6,2,1},{2,1,6},{1,6,2}} can be denoted by {1,2,6}. 

This is not the same as listing partitions because usually at least some
partitions containing the same elements are not equivalent to each other.

E.g. when p=10 and q=4, the compositions {1,2,2,5} cannot be transformed
into {2,1,2,5} by reflection, cycling, or both, because the instances of '2'
are adjacent in one and non-adjacent in the other.

A big thank you for any help with this!

John N


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