Re: cycle index of the group C_2 \wr_k Sym_k
From: Alexander Malkis (alexloeschediesmalk_at_face.cs.uni-sb.de)
Date: 06/02/04
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Date: Wed, 02 Jun 2004 19:00:23 +0200 To: Mitch Harris <harrisq@tcs.inf.tu-dresden.de>
Mitch Harris wrote:
> Alexander Malkis wrote:
>
>> Where it's the autmorphism group of, say, k-dimensional cube, viewed
>> as a graph. The group operates on the edges of this cube.
>> The real problem I'm dealing with is the nxnx...xn-cube in k dimensions.
>>
>> For small n it's done by hand. Maybe somebody has aleady counted this
>> for general n so that we don't need to invent the weel twice.
>
>
> P.W.H. Lemmens, Polya Theory of Hypercubes, Geometriae Dedicata (64) p.
> 145-155.
>
> Gives a method for determining the cycle index for vertices, edges,
> planes, ... any subdimensional simplex.
>
> You'll have to generalize from 2^k to n^k (same conjugacy classes, and
> so same coefficients and exponents, but modified factors in terms.
> (The same reasoning goes for converting the cycle index for vertices to
> the cycle index for other dimensions).
>
Thanks a lot! I've started reading it now.
Regards, Alex
-- Best regards, Alex. PS. To email me, remove "loeschedies" from the email address given.
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