Characterization of the set of values \(f(n)=[n \alpha ], n=1,2,\dots \)

DOI10.1016/0012-365X(72)90012-XzbMath0246.10005OpenAlexW2090062988MaRDI QIDQ2555512

Michael Shimshoni, Jonathan Levitt, Aviezri S. Fraenkel

Publication date: 1972

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(72)90012-x

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Radix representation; digital problems (11A63)

Related Items (14)

A decoding problem in dynamics and in number theory ⋮ The Characterization of Rational Numbers Belonging to a Minimal Path in the Stern-Brocot Tree According to a Second Order Balancedness ⋮ Certain sequences of Wythoffian matrices, and maximal geometric progressions therein ⋮ \(\alpha\)-words and factors of characteristic sequences ⋮ A representation theorem of the suffixes of characteristic sequences ⋮ On the superimposition of Christoffel words ⋮ Locating factors of a characteristic word via the generalized Zeckendorf representation of numbers ⋮ \(Q\)-factorization of suffixes of two-way infinite extensions of irrational characteristic words ⋮ Iterated Floor Function, Algebraic Numbers, Discrete Chaos, Beatty Subsequences, Semigroups ⋮ Substitution invariant Sturmian bisequences ⋮ Positive factors of Wythoff matrices ⋮ Second Order Balance Property on Christoffel Words ⋮ Applications of standard Sturmian words to elementary number theory ⋮ On a theorem of Fraenkel, Levitt and Shimshoni

Cites Work

• A generalization of Wythoff's game
• An L 1 Extremal Problem for Polynomials
• The Bracket Function and Complementary Sets of Integers
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