Permanents of (0,1) matrices :: classification

[wouter meeussen]

error:

n=4 gives 650 when 'baseform' is applied up to fixed point.
That's 10 of those matrices need multiple applications of
'baseform' in order to stabilise.

Sorry there,

Wouter.


----- Original Message -----
From: "Meeussen Wouter (bkarnd)" <wouter.meeussen at vandemoortele.com>
To: "Seqfan (E-mail)" <seqfan at ext.jussieu.fr>
Sent: Thursday, October 30, 2003 1:45 PM
Subject: Permanents of (0,1) matrices :: classification


> seqfanners,
>
> since the Permanent of a (square) (0,1)-matrix is conserved under
> permutation of rows and\or columns,
> one might wonder how many 'base forms' of such matrices exist:
>
>            baseform= sortrows( sortcolumns(sortrows( matrix) ) )
>
> throwing this definition over all (0,1) matrices from 1x1 opto 4x4
> I find:          2,  7,  45,  660
>
> (! EIS : no match!  Huh?
> is this sorting technique too irrelevant? I checked that it 'fixpoints' !)
>
> Superseeker produced only matches thru substitutions & deletions..
>
>
> Wouter.
>
>
> Mma:
> Table[Length at Split[Sort[baseform/@(Partition[#,n]&/@(
> IntegerDigits[Range[0,-1+2^n^2],2,n^2]))]],{n,4}]
>
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> (* corporate gibberish below this line *)
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