Re: Cyclic permutations
- To: mathgroup at smc.vnet.net
- Subject: [mg79493] Re: Cyclic permutations
- From: David Bailey <dave at Remove_Thisdbailey.co.uk>
- Date: Sat, 28 Jul 2007 05:23:13 -0400 (EDT)
- References: <f89r42$664$1@smc.vnet.net>
Bill Rowe wrote:
> On 7/25/07 at 5:27 AM, peter.king at imperial.ac.uk (King, Peter R)
> wrote:
>
>> I have a set of permutations eg.
>
>> {a,b,c,d}, {a,c,b,d} {b,c,d,a}
>
>> Some of which are just cyclic variations of others (ie. {b,c,d,a} is
>> a cyclic variant of {a,b,c,d}). Is there a simple way of getting rid
>> of these, so that the above set just becomes
>
>> {a,b,c,d}, {a,c,b,d}
>
>> I am quite happy to select the cyclic variant to be kept arbitrarily
>> (or using lexical ordering, I'm not particularly concerned).
>
> One way to do this would be to use Union with Signature, i.e.,
>
> In[5]:= Union[{{a, b, c, d}, {a, c, b, d}, {b, c, d, a}},
> SameTest -> (SameQ @@ (Signature /@ {##}) &)]
>
> Out[5]= {{a, b, c, d}, {a, c, b, d}}
> --
> To reply via email subtract one hundred and four
>
Surely this technique would reduce the list to one even permutation, and
one odd one - something quite different! For example:
Union[{{a, b, c, d, e}, {a, c, b, d, e}, {b, c, d, a, e}},
SameTest -> (SameQ @@ (Signature /@ {##}) &)]
David Bailey
http://www.dbaileyconsultancy.co.uk