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A272661
Number of distinct characteristic polynomials of n X n matrices with elements {0, 1}.
14
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
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
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