A127182 Number of distinct characteristic polynomials of n X n real robust {0,1}-matrices.
1, 2, 12, 156, 5612
Offset: 1
Keywords
Examples
a(2)=2 because there are 4 binary robust 2 X 2 matrices, but only two distinct characteristic polynomials, namely y^2-y-1 and y^2-2y+1. a(3)=12 because there are 12 different characteristic polynomials: -1-3y-y^2+y^3, 1-2y-y^2+y^3, 1+y-3y^2+y^3, -2+3y-3y^2+y^3, -1-2y-y^2+y^3, -1-y-y^2+y^3, -1+y-2y^2+y^3, 2-y-2y^2+y^3, -1+2y-3y^2+y^3, 1-y-2y^2+y^3, 1- 2y^2+y^3, -1+3y-3y^2+y^3.
Programs
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Mathematica
mats[1] = {{{1}}}; mats[n_Integer?Positive] := mats[n] = Module[{newrows = Rest[Tuples[{0, 1}, {n}]], mp1 = Flatten[Function[k, Thread[(Append[ #1, #2]&)[ #1, k]]& /@ mats[n - 1]] /@ Tuples[{0, 1}, {n - 1}], 1]}, Flatten[MapThread[Function[{m, nl}, Append[m, # ]& /@ nl], {mp1, Pick[newrows, # =!= 0& /@ # ]& /@ (First /@ Dot[NullSpace /@ mp1, Transpose[newrows]])}], 1]] A127182[n_]=Length[Union[CharacteristicPolynomial[mats[n]]]]