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

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

Offset

0,2

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

Table of n, a(n) for n=0..6.

Robert M. Corless, Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, Venkat Balasubramanian, Slides from "Bohemian Eigenvalues" talk.

Robert Israel, Examples for n=5

Prog

(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

Crossrefs

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

Sequence in context: A354847 A123903 A172401 * A005742 A055612 A236691

Adjacent sequences: A272658 A272659 A272660 * A272662 A272663 A272664

Keyword

nonn,more

Author

N. J. A. Sloane, May 15 2016

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

Status

approved