Generalizing Zeckendorf's theorem to \(f\)-decompositions

DOI10.1016/j.jnt.2014.01.028zbMath1309.11013arXiv1309.5599OpenAlexW2011494645MaRDI QIDQ402633

Archit Kulkarni, Steven J. Miller, Umang Varma, Philippe Demontigny, David Moon, Thao T. Do

Publication date: 28 August 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.5599

zbMATH Keywords

recurrence relationsStirling numbers of the first kindZeckendorf decompositionsGaussian behavior

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Convergence of probability measures (60B10) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (10)

The Fibonacci Sequence and Schreier-Zeckendorf Sets ⋮ On Zeckendorf Related Partitions Using the Lucas Sequence ⋮ Patterns in variations of the Fibonacci sequence ⋮ Zeckendorf representation of multiplicative inverses modulo a Fibonacci number ⋮ Average number of Zeckendorf integers ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Bin decompositions ⋮ The distribution of gaps between summands in generalized Zeckendorf decompositions ⋮ A Probabilistic Approach to Generalized Zeckendorf Decompositions

Cites Work

• From Fibonacci numbers to central limit type theorems
• The distribution of gaps between summands in generalized Zeckendorf decompositions
• Gaussian limiting distributions for the number of components in combinatorial structures
• The algebraic structure of linearly recursive sequences under Hadamard product
• Contributions to digit expansions with respect to linear recurrences
• The distribution of the sum-of-digits function
• Generalized Zeckendorf expansions
• Corrigendum to ``Generalized Zeckendorf expansions
• A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers
• On the number of summands in Zeckendorf decompositions
• Differences of Multiple Fibonacci Numbers
• Gaussian Behavior in Generalized Zeckendorf Decompositions
• The Average Gap Distribution for Generalized Zeckendorf Decompositions
• Representation of Natural Numbers as Sums of Generalised Fibonacci Numbers
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