Number of matrices n x n with n^2 different elements which have that same characteristic polynomial
Artur
grafix at csl.pl
Tue Jan 9 18:15:23 CET 2007
Thanks for Max! Good is:
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
12 matrices with 9 distinct elements which have that same characteristic
polynomial
{{a,d,e},{f,b,g},{h,i,c}}
{{a,f,h},{d,b,i},{e,g,c}}
{{a,e,d},{h,c,i},{f,g,b}}
{{a,h,f},{e,c,g},{d,i,b}}
{{b,d,i},{f,a,h},{g,e,c}}
{{b,f,g},{d,a,e},{i,h,c}}
{{b,g,f},{i,c,h},{d,e,a}}
{{b,i,d},{g,c,e},{f,h,a}}
{{c,e,g},{h,a,f},{i,d,b}}
{{c,h,i},{e,a,d},{g,f,b}}
{{c,g,e},{i,b,d},{h,f,a}}
{{c,i,h},{g,b,f},{e,d,a}}
Problem is for 4 x 4 because loops have 4! 12!=344881152000 steps and is
out of possibility of my computer
ARTUR
More information about the SeqFan
mailing list