منابع مشابه
Zeckendorf family identities generalized
This is a detailed version of my text [2]. It contains the proof outlined in [2] in much more detail and was written for the purpose of persuading myself that my proofs are correct. This note has never been proofread by myself or anyone else. If you find any mistakes or typos, please inform me at ∆Γ@gmail.com where ∆ =darij and Γ =grinberg Thank you! Definitions. 1) A subset S of Z is called ho...
متن کاملZeckendorf family identities generalized
This is a brief version of my text [2]. For more detailed proofs, see [2] (but beware that [2] is sometimes over-precise and very boring). This note has never been proofread by myself or anyone else. If you find any mistakes or typos, please inform me at ∆Γ@gmail.com where ∆ =darij and Γ =grinberg Thank you! The purpose of this note is to establish a generalization of the so-called Zeckendorf f...
متن کاملA Probabilistic Approach to Generalized Zeckendorf Decompositions
Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-b expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence. The expansions are finite sequences of nonnegative integer coefficients (satisfying certain technical conditions to guarantee uniqueness of the decomposition) an...
متن کاملGaussian Behavior in Generalized Zeckendorf Decompositions
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers {Fn}n=1; Lekkerkerker proved that the average number of summands for integers in [Fn,Fn+1) is n/(φ2 + 1), with φ the golden mean. This has been generalized to certain classes of linear recurrence relations, where using techniques from number theory and ergodic theory...
متن کاملThe distribution of gaps between summands in generalized Zeckendorf decompositions
Zeckendorf proved any integer can be decomposed uniquely as a sum of non-adjacent Fibonacci numbers, Fn. Using continued fractions, Lekkerkerker proved the average number of summands of an m ∈ [Fn, Fn+1) is essentially n/(φ + 1), with φ the golden ratio. This result has been generalized by many, often using Markov processes, to show that for any positive linear recurrence the number of summands...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1994
ISSN: 0893-9659
DOI: 10.1016/0893-9659(94)90025-6