First Occurrence Of Floor(m/d(m))

[hv at crypt.org]

Dear Seqfans
Who is able help me find mistake in Mathematica procedure
  for case 3 x 3 Number of matrices n x n with n^2 different elements which  
have that same characteristic polynomial

p = Permutations[{a, b, c}]; q = Permutations[{d, e, f, g, h, i}];
      m = 0; s = {{a, d, e}, {f, b, g}, {h, i, c}};
Do[Do[{{r = p[[x, 1]], q[[y, 1]], q[[y, 2]]}, {q[[y, 3]], p[[x,
       2]], q[[y, 4]]}, {q[[y, 5]], q[[y, 6]], p[[x, 3]]}}; If[
     CharacteristicPolynomial[r, n] == CharacteristicPolynomial[s,
           n], m++; Print[r]], {y, 1, Length[q]}], {x, 1, Length[p]}]; m

Is somethink wrong because final result have to give m=12 but is giving m=0

For any help I would like to thank on advance!

ARTUR


>
> Dnia 09-01-2007 o 07:24:06 Max A. <maxale at gmail.com> napisał(a):
>
>> It is easy to see that every element of this sequence a(n) is a
>> multiple of 2*n! (for n>1) and a divisor of (n^2)!.
>>
>> In particular, for n>1, 2*n! divides a(n) since simultaneous
>> permutations of rows and columns (of the total number n!) of a matrix
>> do not change its characteristic polynomial and neither do
>> transpositions (bringing the factor of 2). Moreover, b(n)=a(n)/(2*n!)
>> gives the number of non-equivalent (in terms of simultaneous
>> permutations of rows and columns, and transpositions) with equal
>> characteristic polynomials.
>>
>> Every characteristic polynomial of n x n matrices on the same set of
>> n^2 variables appears exactly a(n) times, implying that a(n) divides
>> (n^2)!. The number of distinct characteristic polynomials is given by
>> c(n)=(n^2)!/a(n).
>>
>> Now, fixing elements on the main diagonal, it can be shown that
>> binomial(n^2,n) divides c(n), implying that a(n) divides n!*(n^2-n)!
>> and that b(n) divides (n^2-n)!/2.
>>
>> These are the values of a(n), b(n), and c(n) for n=1,2,3:
>> a(n): 1, 4, 12
>> b(n): 1, 1, 1
>> c(n): 1, 6, 30240
>>
>> Max
>>
>> On 1/8/07, Artur <grafix at csl.pl> wrote:
>>> Dear Seqfans,
>>> I'm asking: How many different matrices n x n with n^2 different  
>>> elements
>>> occured which have that same characteristic polynomial
>>> We have to count all permutations n^2 elements in n x n matrix and  
>>> count
>>> only these permutations
>>> which don't changed starting polynomial
>>> for 2 x 2 case
>>> we have 4 matrices X^2-(a+d)X+ad-bc
>>> a b   a c   d c   d b
>>> c d   b d   b a   c a
>>>
>>> BEST WISHES
>>> ARTUR
>>>
>>>
>
>
>
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