On a family of tridiagonal matrices

Roland Bacher (1)

1 IF - Institut Fourier

We show that certain integral positive definite symmetric tridiagonal matrices of determinant $n$ are in one to one correspondence with elements of $(\mathbb Z/n\mathbb Z)^*$. We study some properties of this correspondence. In a somewhat unrelated second part we discuss a construction which associates a sequence of integral polytopes to every integral symmetric matrix.

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]

Roland Bacher. On a family of tridiagonal matrices. 2008. ⟨hal-00319587⟩