OFFSET
0,3
COMMENTS
REFERENCES
E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Am. Math. Soc. Translations, Series 2, Vol. 6, 1957.
LINKS
Chao Ju, Chern-Simons Theory, Ehrhart Polynomials, and Representation Theory, arXiv:2304.11830 [math-ph], 2023. See p. 14.
Wikipedia, Special unitary group
FORMULA
Conjecture: det(M(n)) = A000272(n+1).
The conjecture is true (see proof in Links). - Stefano Spezia, May 24 2023
EXAMPLE
a(3) = 72:
[3, 2, 1]
M(3) = [2, 4, 2]
[1, 2, 3]
a(5) = 140400:
[5, 4, 3, 2, 1]
[4, 8, 6, 4, 2]
M(5) = [3, 6, 9, 6, 3]
[2, 4, 6, 8, 4]
[1, 2, 3, 4, 5]
MAPLE
a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](
Matrix(n, (i, j)-> min(i, j)*(n+1)-i*j))):
seq(a(n), n=0..16); # Alois P. Heinz, Apr 30 2023
MATHEMATICA
M[i_, j_, n_]:=Min[i, j](n+1)-i j; Join[{1}, Table[Permanent[Table[M[i, j, n], {i, n}, {j, n}]], {n, 17}]]
PROG
(PARI) a(n) = matpermanent(matrix(n, n, i, j, min(i, j)*(n + 1) - i*j)); \\ Michel Marcus, Apr 30 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Apr 29 2023
STATUS
approved