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

[franktaw at netscape.net]

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.