Matrices autosimilaires

Roland Bacher (1)

1 IF - Institut Fourier

We describe a class of matrices whose determinants are trivial to compute. A nice example of such a matrix is given by considering the symmetric matrix with entries {i+j choose i} (mod 2) in {0,1}, 0 <= i,j < n the binomial coefficients modulo 2 represented by {0,1}. The determinant of the above matrix is then closely related to the Thue-Morse sequence counting digits modulo 2 of binary integers.

Domaines: Anneaux et algèbres [math.RA]; Combinatoire [math.CO]; Théorie des nombres [math.NT]

Roland Bacher. Matrices autosimilaires. 2002. ⟨hal-00012438⟩