A272658 Number of distinct characteristic polynomials of n X n matrices with elements {-1, 0, +1}.
1, 3, 16, 209, 8739, 1839102
Offset: 0
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
- Eunice Y. S. Chan, Algebraic Companions and Linearizations, The University of Western Ontario (Canada, 2019) Electronic Thesis and Dissertation Repository. 6414.
- Eunice Y. S. Chan and Robert Corless, A new kind of companion matrix, Electronic Journal of Linear Algebra, Volume 32, Article 25, 2017, see p. 335.
- Robert M. Corless et al., Bohemian Eigenvalues.
- Robert Corless and Steven Thornton, The Bohemian Eigenvalue Project, 2017 poster.
Crossrefs
Programs
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Mathematica
a[n_] := a[n] = Module[{m, cPolys}, m = Tuples[Tuples[{-1, 0, 1}, n], n]; cPolys = CharacteristicPolynomial[#, x] & /@ m; Length[DeleteDuplicates[cPolys]]]; Table[a[i], {i, 1, 3}] (* Robert P. P. McKone, Sep 16 2023 *) -
Python
from itertools import product from sympy import Matrix def A272658(n): return len({tuple(Matrix(n,n,p).charpoly().as_list()) for p in product((-1,0,1),repeat=n**2)}) if n else 1 # Chai Wah Wu, Sep 30 2023
Formula
a(n) <= 3^(n^2). - Robert P. P. McKone, Sep 16 2023
Extensions
a(4) found by Daniel Lichtblau, May 13 2016
a(5) found by Daniel Lichtblau and Steven E. Thornton, May 19 2016
a(0)=1 prepended by Alois P. Heinz, Sep 28 2023