A272662 Number of distinct characteristic polynomials of n X n matrices with elements {-1, +1}.

1, 2, 6, 28, 203, 3150, 131641

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.)

Crossrefs

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

Programs

Python

from itertools import product
from sympy import Matrix
def A272662(n): return len({tuple(Matrix(n,n,p).charpoly().as_list()) for p in product((-1,1),repeat=n**2)}) if n else 1 # Chai Wah Wu, Sep 30 2023

Extensions

a(5) and a(6) from Steven E. Thornton, Mar 09 2019

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