Learn More
The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see [1]). We present a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a Töeplitz matrix and a unipotent upper triangular matrix. The determinant of a generalized Pascal matrix equals thus the(More)
The purpose of this article is to obtain some new infinite families of Toeplitz matrices, 7-matrices and generalized Pascal triangles whose leading principal minors form the Fibonacci, Lucas, Pell and Jacobsthal sequences. We also present a new proof for Theorem 3.1 in [R. Bacher. Determinants of matrices related to the Pascal triangle. J. Théor. Nombres(More)
Let φ = (φ i) i≥1 and ψ = (ψ i) i≥1 be two arbitrary sequences with φ 1 = ψ 1. Let A φ,ψ (n) denote the matrix of order n with entries a i,j , 1 ≤ i, j ≤ n, where a 1,j = φ j and a i,1 = ψ i for 1 ≤ i ≤ n, and where a i,j = a i−1,j−1 + a i−1,j for 2 ≤ i, j ≤ n. It is of interest to evaluate the determinant of A φ,ψ (n), where one of the sequences φ or ψ is(More)
The purpose of this article is to obtain some new infinite families of Toeplitz matrices , 7-matrices and generalized Pascal triangles whose leading principal minors form the Fibonacci, Lucas, Pell and Jacobsthal sequences. We also present a new proof for Theorem 3.1 in [R. Bacher. Determinants of matrices related to the Pascal triangle. In memory of(More)
Let φ = (φi)i≥1 and ψ = (ψi)i≥1 be two arbitrary sequences with φ1 = ψ1. Let Aφ,ψ(n) denote the matrix of order n with entries ai,j , 1 ≤ i, j ≤ n, where a1,j = φj and ai,1 = ψi for 1 ≤ i ≤ n, and where ai,j = ai−1,j−1 + ai−1,j for 2 ≤ i, j ≤ n. It is of interest to evaluate the determinant of Aφ,ψ(n), where one of the sequences φ or ψ is the Fibonacci(More)
The spectrum ω(G) of a finite group G is the set of element orders of G. If Ω is a non-empty subset of the set of natural numbers, h(Ω) stands for the number of isomorphism classes of finite groups G with ω(G) = Ω and put h(G) = h(ω(G)). We say that G is recognizable (by spectrum ω(G)) if h(G) = 1. The group G is almost recognizable (resp. nonrecognizable)(More)
  • 1