Re: 'necklace'-type classes of combinatorial compositions

["Max Alekseyev" <maxale@gmail.com>]

Yeah, sorry about this bug.
Hopefully, the attached version has no bugs.

Regards,
Max

On 6/9/07, john n <johnnagelson@yahoo.co.uk> wrote:
> Thanks very much for your amazingly quick help with this.
>
> But your implementation lists some classes more than once. E.g:
>
> ? par_all(7,4)
>
> [1, 1, 1, 4]
> [1, 1, 2, 3]
> [1, 1, 3, 2]
> [1, 2, 1, 3]
> [1, 2, 2, 2]
>
> ...but [1, 1, 2, 3] and [1, 1, 3, 2] are equivalent under a combination of
> reflection and cycling.
>
> Thanks again - I am very grateful!
>
> Cheers,
>
> John
>
>
>
>
> Max A. wrote:
> >
> > My quick-n-dirty implementation is attached.
> > Function par_all() iterates over the smallest lexicographical
> > representatives of each equivalence class and calls process() function
> > for every such representative. Currently process() simply prints out
> > its argument. E.g.:
> >
> > ? par_all(9,3)
> > [1, 1, 7]
> > [1, 2, 6]
> > [1, 6, 2]
> > [1, 3, 5]
> > [1, 5, 3]
> > [2, 2, 5]
> > [1, 4, 4]
> > [2, 3, 4]
> > [2, 4, 3]
> > [3, 3, 3]
> >
> > Regards,
> > Max
> >
> > On 6/9/07, john n <johnnagelson@yahoo.co.uk> wrote:
> >>
> >> 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
> >>
> >>
> >> --
> >> View this message in context:
> >> http://www.nabble.com/%27necklace%27-type-classes-of-combinatorial-compositions-tf3895323.html#a11043232
> >> Sent from the cr.yp.to - pari-users mailing list archive at Nabble.com.
> >>
> >>
> >
> >
> >
>
> --
> View this message in context: http://www.nabble.com/%27necklace%27-type-classes-of-combinatorial-compositions-tf3895323.html#a11044329
> Sent from the cr.yp.to - pari-users mailing list archive at Nabble.com.

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