[seqfan] Re: A generalization of the matrix permanent: question

franktaw at netscape.net franktaw at netscape.net
Fri Apr 3 00:52:42 CEST 2009

Well, if you sum over the alternating group, you get the average (mean) 
of the permanent and the determinant.

Summing over the cyclic group just includes each term in the matrix in 
a single product, one product for each modular diagonal; I doubt that 
there's much interest there.  There may be some value in summing over 
the dihedral group.

(As to your question, I have no idea if there's any literature on this.)

Franklin T. Adams-Watters

-----Original Message-----
From: Simone Severini <simoseve at gmail.com>

Dear SeqFans,

I have a question concerning matrix permanents.

The definition of the permanent contains a product and a sum. The sum
is taken over all elements of the full symmetric group on n symbols,
where n is the size of the matrix.

Do you know of any generalization in which the sum is taken over a
subset, or possibly a subgroup, of the full symmetric group?

I have quickly searched the literature, but I could not find much,
probably because I did not look for the right thing.

If this generalization of the permanent has not been studied, it may
be worth a look.

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