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Komornik–Loreti constant, the Glossary

Index Komornik–Loreti constant

In the mathematical theory of non-standard positional numeral systems, the Komornik–Loreti constant is a mathematical constant that represents the smallest base q for which the number 1 has a unique representation, called its q-development.[1]

Table of Contents

  1. 11 relations: Euler's constant, Fibonacci word, Floor and ceiling functions, Greedy algorithm, Mathematical constant, Non-integer base of numeration, Paola Loreti, Prouhet–Thue–Morse constant, Rudin–Shapiro sequence, Thue–Morse sequence, Transcendental number.

  2. Non-standard positional numeral systems

Euler's constant

Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma, defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by: \begin \gamma &. Komornik–Loreti constant and Euler's constant are mathematical constants.

See Komornik–Loreti constant and Euler's constant

Fibonacci word

A Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet).

See Komornik–Loreti constant and Fibonacci word

Floor and ceiling functions

In mathematics, the floor function is the function that takes as input a real number, and gives as output the greatest integer less than or equal to, denoted or.

See Komornik–Loreti constant and Floor and ceiling functions

Greedy algorithm

A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage.

See Komornik–Loreti constant and Greedy algorithm

Mathematical constant

A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Komornik–Loreti constant and mathematical constant are mathematical constants.

See Komornik–Loreti constant and Mathematical constant

Non-integer base of numeration

A non-integer representation uses non-integer numbers as the radix, or base, of a positional numeral system. Komornik–Loreti constant and non-integer base of numeration are non-standard positional numeral systems.

See Komornik–Loreti constant and Non-integer base of numeration

Paola Loreti

Paola Loreti is an Italian mathematician, and a professor of mathematical analysis at Sapienza University of Rome.

See Komornik–Loreti constant and Paola Loreti

Prouhet–Thue–Morse constant

In mathematics, the Prouhet–Thue–Morse constant, named for, Axel Thue, and Marston Morse, is the number—denoted by —whose binary expansion 0.01101001100101101001011001101001... Komornik–Loreti constant and Prouhet–Thue–Morse constant are mathematical constants.

See Komornik–Loreti constant and Prouhet–Thue–Morse constant

Rudin–Shapiro sequence

In mathematics, the Rudin–Shapiro sequence, also known as the Golay–Rudin–Shapiro sequence, is an infinite 2-automatic sequence named after Marcel Golay, Harold S. Shapiro, and Walter Rudin who investigated its properties.

See Komornik–Loreti constant and Rudin–Shapiro sequence

Thue–Morse sequence

In mathematics, the Thue–Morse or Prouhet–Thue–Morse sequence is the binary sequence (an infinite sequence of 0s and 1s) that can be obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far.

See Komornik–Loreti constant and Thue–Morse sequence

Transcendental number

In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients.

See Komornik–Loreti constant and Transcendental number

See also

Non-standard positional numeral systems

References

[1] https://en.wikipedia.org/wiki/Komornik–Loreti_constant