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Showing 1 to 9 of 9 for “"Fibonacci sequence"”.
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The Z-densities of the Fibonacci Sequence
… made a conjecture about the Z-densities of the Fibonacci sequence, F(n), based on computational results. For a prime p, Z(p) is the ``Fibonacci entry-point of n" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is less than x such that m divides Z(p), …
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Integer Compositions, Gray Code, and the Fibonacci Sequence
… and Gray Code to integer compositions and the Fibonacci sequence through the use of analytic combinatorics, Zeckendorf's Theorem, and generating functions.</p>
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Fibonacci sequences
… in the thirteenth century, Leonardo de Pisa, or, Fibonacci, introduced his famous rabbit problem, which may be stated simply as follows: assume that rabbits reproduce at a rate such that one pair is born each month from each pair of adults not less than two months old. If one pair is present …
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Around the Fibonacci Numeration System
Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can …
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Elgenvalues of Fibonacci-like Sequences
The familiar Fibonacci sequence 1,1,2,3,5,8,13,... can be described by the recurrence relation x(0) = 1, x(1) = 1, x(n) = x(n-1) + x(n-2). For this relation, as n → oo, x(n+1) → 1 +√5 x(n) 2 ' which is the familiar golden ratio. This value is also the dominant eigenvalue of the above recurrence …
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Prime And Irreducible Elements In Z<sub>x</sub> , Hamiltonian Cycles In Concentric Circle Graphs, And Fibonacci Sequences In Z<sub>x</sub>
… circle graphs. In the third part, we discuss the Fibonacci sequence in Z<sub>x</sub>. All of the theorems stated in our thesis are new to us.
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Differential posets and dual graded graphs
… posets. In particular, we prove that the rank sequence of an r-differential poset is bounded above by the Fibonacci sequence and that there is a unique poset with such a maximum rank sequence. We also prove that a 1-differential lattice is either Young's lattice or the Fibonacci lattice. In the …
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Broken Gourd
… process using a set of numbers derived from a fibonacci sequence I make the ensemble gradually grow in intensity. It builds up until reaching a climax right at the moment where the gourd is dropped and breaks, leading to the resolution of the piece that portrays the earth being filled with …
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New Psalms for S.S.A.A.T.T.B.B. Chorus, A Capella
… notes unfold via a process influenced by the Fibonacci Sequence and the Lucas Sequence, creating a sonic flux of ebb and flows dictated by the order of the sequences. The numbers are known for their association with underlying geometrical proportions in nature and biology. Their mathematical …