A Note on Closed-Form Representation of Fibonacci Numbers Using Fibonacci Trees
TL;DR: In this paper, a new representation of the Fibonacci numbers was given using Fibonaccia trees and with the help of this new representation, the th-fibonacci number can be calculated without having any knowledge about the previous numbers.
Abstract: We give a new representation of the Fibonacci numbers. This is achieved using Fibonacci trees. With the help of this
representation, the th Fibonacci number can be calculated without
having any knowledge about the previous Fibonacci numbers.
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TL;DR: The result shows that an algorithm with Fibonacci trees as underlying data structure can be implemented concurrently on a hypercube network with no communication latency.
Abstract: The Fibonacci tree is a rooted binary tree whose number of vertices admit a recursive definition similar to the Fibonacci numbers. In this paper, we prove that a hypercube of dimension admits two edge-disjoint Fibonacci trees of height , two edge-disjoint Fibonacci trees of height , two edge-disjoint Fibonacci trees of height and so on, as subgraphs. The result shows that an algorithm with Fibonacci trees as underlying data structure can be implemented concurrently on a hypercube network with no communication latency.
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14 Jan 1963
TL;DR: The organization of information placed in the points of an automatic computer is discussed and the role of memory, storage and retrieval in this regard is discussed.
Abstract: : The organization of information placed in the points of an automatic computer is discussed. (Author)
846 citations