Showing papers on "Fibonacci number published in 1974"
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81 citations
TL;DR: In this article, a recursive procedure is developed that makes it possible to determine all conjugacy classes under both SO(p,q) and O(p + q ≤ 6.
Abstract: A recursive procedure is developed that makes it possible to determine all conjugacy classes under both SO(p,q) and O(p,q) of the maximal solvable subalgebras of the Lie algebras LO(p,q) [and the continuous maximal solvable subgroups of SO(p,q)]. The cases of greatest physical interest with p ≥ q ≥ 0 and p + q ≤ 6 are considered in detail (they include the Lorentz group, de Sitter groups, and the conformal group of space‐time). Formulas (in terms of Fibonacci numbers) are given for the number of O(p,q) [and SO(p,q)] equivalence classes of maximal solvable subalgebras of LO(p,q).
26 citations
TL;DR: In this paper, it was shown that the groups F(2, 8) and F( 2, 10) are infinite, and that the only Fibonacci group whose finiteness or infiniteness has not been determined has not yet been determined.
Abstract: Fibonacci groups are the groupswhere r is a natural number. The groups F(2, 8) and F(2, 10) are shown to he infinite, thus leaving F(2, 9) as the only Fibonacci group whose finiteness or infiniteness has not been determined.
17 citations
TL;DR: The so-called Fibonacci groups were introduced by Conway in [1] and a more general class of groups is investigated in this article, where the derived factor-groups of the groups in the latter class are studied.
Abstract: The so-called Fibonacci groups were introduced by Conway in [1]; a more general class of groups is investigated in [2]. In this article, we consider the derived factor-groups of the groups in the latter class, and use two different presentations of them, first to prove that they are all finite and second to give formulae for their orders.
15 citations
TL;DR: Some Congruences of the Fibonacci Numbers Modulo a Prime p. 210-214 as mentioned in this paper was the first paper to explore the relationship between the modulo a prime and the number modulo.
Abstract: (1974). Some Congruences of the Fibonacci Numbers Modulo a Prime p. Mathematics Magazine: Vol. 47, No. 4, pp. 210-214.
10 citations
01 Jan 1974
TL;DR: The problem considered in this chapter is that of minimizing the value E = f(x) = f (x) so that the total number of bits in the solution to the inequality of the following type is minimized.
Abstract: The problem considered in this chapter is that of minimizing the value
$$ {\text{minimize}}\,E = f(x). $$
1 citations
TL;DR: An intuitively appealing derivation of the Fibonacci searching algorithm is presented in this article, where a new equation is developed to determine appropriate test points for the FIFO algorithm.
Abstract: An intuitively appealing derivation of the Fibonacci searching algorithm is presented. A new equation is developed to determine appropriate test points for Fibonacci searching.