Generalized Zeckendorf expansions

DOI10.1016/0893-9659(94)90025-6zbMath0792.11002OpenAlexW2068560453WikidataQ126758579 ScholiaQ126758579MaRDI QIDQ1324464

Attila Pethoe, Peter J. Grabner, Robert F. Tichy, István Nemes

Publication date: 31 July 1994

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0893-9659(94)90025-6

zbMATH Keywords

linear recurrencesPisot numbersfinite representationsdigit expansions\(\beta\)-shiftPisot recurrences

Mathematics Subject Classification ID

Recurrences (11B37) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Other number representations (11A67)

Related Items (17)

Associativity of recurrence multiplication ⋮ Exploiting geometric signatures to accurately determine properties of attractors ⋮ Numbers with fixed sum of digits in linear recurrent number systems ⋮ On Zeckendorf Related Partitions Using the Lucas Sequence ⋮ Combinatorial constructions for the Zeckendorf sum of digits of polynomial values ⋮ Generalizing Zeckendorf's theorem to \(f\)-decompositions ⋮ From Fibonacci numbers to central limit type theorems ⋮ Zeckendorf representation of multiplicative inverses modulo a Fibonacci number ⋮ Average number of Zeckendorf integers ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The distribution of gaps between summands in generalized Zeckendorf decompositions ⋮ The weak converse of Zeckendorf's theorem ⋮ Unique representations of integers using increasing sequences ⋮ A Probabilistic Approach to Generalized Zeckendorf Decompositions ⋮ The sum of digits function of the base phi expansion of the natural numbers ⋮ Summand minimality and asymptotic convergence of generalized Zeckendorf decompositions

Cites Work

• Contributions to digit expansions with respect to linear recurrences
• On digit expansions with respect to linear recurrences
• \(\beta\)-expansions and symbolic dynamics
• Finite beta-expansions
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Systems of Numeration
• On Periodic Expansions of Pisot Numbers and Salem Numbers
• Representations of numbers and finite automata
• On algebraic equations with all but one root in the interior of the unit circle. To my teacher and former colleague Erhard Schmidt on his 75th birthday
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