Re: Cyclic permutations
- To: mathgroup at smc.vnet.net
- Subject: [mg79534] Re: Cyclic permutations
- From: Bill Rowe <readnewsciv at sbcglobal.net>
- Date: Sat, 28 Jul 2007 05:44:29 -0400 (EDT)
On 7/27/07 at 6:04 AM, drmajorbob at bigfoot.com (DrMajorBob) wrote:
>Won't that SameTest equate a lot of permutations that aren't the
>"same" in the OP's requested sense?
>perms = Permutations[Range@4] Signature /@ perms Union[perms,
>SameTest -> (SameQ @@ (Signature /@ {##}) &)]
>{{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 2, 4}, {1, 3, 4, 2}, {1, 4, 2,
>3}, {1, 4, 3, 2}, {2, 1, 3, 4}, {2, 1, 4, 3}, {2, 3, 1, 4}, {2, 3,
>4, 1}, {2, 4, 1, 3}, {2, 4, 3, 1}, {3, 1, 2, 4}, {3, 1, 4, 2}, {3,
>2, 1, 4}, {3, 2, 4, 1}, {3, 4, 1, 2}, {3, 4, 2, 1}, {4, 1, 2, 3},
>{4, 1, 3, 2}, {4, 2, 1, 3}, {4, 2, 3, 1}, {4, 3, 1, 2}, {4, 3, 2, 1}}
>{1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1,
>\ 1, 1, -1, -1, 1}
>{{1, 2, 3, 4}, {1, 2, 4, 3}}
>Only two distinct permutations exist (for ANY list) with that
>SameTest.
>I thought the OP wanted something like
>Union[perms /. {a__, 1, b___} :> {1, b, a}]
>{{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 2, 4}, {1, 3, 4, 2}, {1, 4, 2,
>3}, {1, 4, 3, 2}}
I think your assessment is correct. I had thought Signature
returned different values for permutations that were not cyclic
versions of each other. I see on looking at the documentation
this isn't the case. Sorry for the confusion I perhaps caused.
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