A272661 Number of distinct characteristic polynomials of n X n matrices with elements {0, 1}.

1, 2, 6, 32, 333, 8927, 758878

Offset: 0

Author

N. J. A. Sloane, May 15 2016

Keywords

• nonn
• more

References

• Robert M. Corless, Bohemian Eigenvalues, Talk Presented at Computational Discovery in Mathematics (ACMES 2), University of Western Ontario, May 12 2016. (Talk based on joint work with Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, Venkat Balasubramanian.)

Links

• Robert M. Corless, Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, Venkat Balasubramanian, Slides from "Bohemian Eigenvalues" talk.
• Robert Israel, Examples for n=5

Crossrefs

Six classes of matrices mentioned in Rob Corless's talk: A272658, A272659, A272660, A272661, A272662, A272663.

Programs

MATLAB

function count = A272661(N)
  C = zeros(0,N);
  count = 0;
  V = zeros(1,N);
  L = -floor(N/2) + [0:N-1];
  for x = 0:2^(N^2)-1;
    r = dec2bin(x+2^(N^2))-'0';
    A = reshape(r(2:end),N,N);
    rowcounts = sum(A,2);
    colcounts = sum(A,1);
    if ~issorted(rowcounts)|| rowcounts(N) < max(colcounts)
      continue
    end
    for i = 1:N
        V(i) = round(det(A - L(i)*eye(N)));
    end
    if ~ismember(V, C, 'rows')
      count = count+1;
      C(count,:) = V;
    end
  end
end  % Robert Israel, Aug 18 2016

Python

from itertools import product
from sympy import Matrix
def A272661(n): return len({tuple(Matrix(n,n,p).charpoly().as_list()) for p in product((0,1),repeat=n**2)}) if n else 1 # Chai Wah Wu, Sep 30 2023

Extensions

a(5) from Robert Israel, Aug 18 2016

a(6) from Steven E. Thornton, Mar 09 2019

a(0)=1 prepended by Alois P. Heinz, Sep 28 2023