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The purpose of this article is to prove several evaluations of determinants of matrices, the entries of which are given by the recurrence a i,j = a i−1,j−1 +a i−1,j , i, j ≥ 2, with various choices for the first row a 1,j and first column a i,1. 1. Introduction. Determinants have played a significant part in various areas in mathematics. For instance, they(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 = (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 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)
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