Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Download
Faster access than browser!
 

Thue–Morse sequence

Index Thue–Morse sequence

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

86 relations: A priori probability, Alan D. Taylor, American Journal of Physics, American Mathematical Monthly, American Mathematical Society, Arithmetic progression, Automatic sequence, Axel Thue, Évariste Galois, Binary number, Binomial theorem, Bit, Bitstream, Bitwise operation, Boat rigging, Boolean algebra, Brewed coffee, Cambridge University Press, Chess, Combinatorics on words, Complex Systems (journal), Concentration, Continuous function, Critical exponent of a word, Degree of a polynomial, Dejean's theorem, Derivative, Differential geometry, Discrete Applied Mathematics, Disjoint sets, Ethiopian cuisine, Evil number, Exclusive or, Fabius function, Fair division, Fixed point (mathematics), Flat function, Formal power series, Fractals (journal), Free monoid, Function (mathematics), Gesine Reinert, GF(2), Gradient, Grandmaster (chess), Hamming weight, Hans Rademacher, John Horton Conway, Kayles, Koch snowflake, ..., L (complexity), L-system, List of Latin phrases (E), Marston Morse, Mathematics, Max Euwe, Monotonic function, Morphic word, Nimber, Nonlinear system, Number theory, Odious number, Orthogonality, Palindromic number, Partition of a set, Periodic sequence, Polynomial, Port and starboard, Prouhet–Tarry–Escott problem, Prouhet–Thue–Morse constant, Recurrence relation, Recurrent word, Recursion, Rowing (sport), Set (mathematics), Sprague–Grundy theorem, Springer Science+Business Media, Square-free word, Step function, Steven Brams, Streetball, Teacher, Threefold repetition, Turtle graphics, Walsh function, Wojciech Szpankowski. Expand index (36 more) »

A priori probability

An a priori probability is a probability that is derived purely by deductive reasoning.

New!!: Thue–Morse sequence and A priori probability · See more »

Alan D. Taylor

Alan Dana Taylor (born October 27, 1947) is an American mathematician who, with Steven Brams, solved the problem of envy-free cake-cutting for an arbitrary number of people with the Brams–Taylor procedure.

New!!: Thue–Morse sequence and Alan D. Taylor · See more »

American Journal of Physics

The American Journal of Physics is a monthly, peer-reviewed scientific journal published by the American Association of Physics Teachers and the American Institute of Physics.

New!!: Thue–Morse sequence and American Journal of Physics · See more »

American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

New!!: Thue–Morse sequence and American Mathematical Monthly · See more »

American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

New!!: Thue–Morse sequence and American Mathematical Society · See more »

Arithmetic progression

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

New!!: Thue–Morse sequence and Arithmetic progression · See more »

Automatic sequence

In mathematics and theoretical computer science, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants to indicate that the base of the numerals used is k) is an infinite sequence of terms characterized by a finite automaton.

New!!: Thue–Morse sequence and Automatic sequence · See more »

Axel Thue

Axel Thue (19 February 1863 – 7 March 1922), was a Norwegian mathematician, known for highly original work in diophantine approximation, and combinatorics.

New!!: Thue–Morse sequence and Axel Thue · See more »

Évariste Galois

Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.

New!!: Thue–Morse sequence and Évariste Galois · See more »

Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

New!!: Thue–Morse sequence and Binary number · See more »

Binomial theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

New!!: Thue–Morse sequence and Binomial theorem · See more »

Bit

The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

New!!: Thue–Morse sequence and Bit · See more »

Bitstream

A bitstream (or bit stream), also known as binary sequence, is a sequence of bits.

New!!: Thue–Morse sequence and Bitstream · See more »

Bitwise operation

In digital computer programming, a bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits.

New!!: Thue–Morse sequence and Bitwise operation · See more »

Boat rigging

Boats used in the sport of rowing may be adjusted in many different ways according to the needs of the crew, the type of racing, and anticipated rowing conditions.

New!!: Thue–Morse sequence and Boat rigging · See more »

Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

New!!: Thue–Morse sequence and Boolean algebra · See more »

Brewed coffee

Brewed coffee is made by pouring hot water onto ground coffee beans, then allowing to brew.

New!!: Thue–Morse sequence and Brewed coffee · See more »

Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

New!!: Thue–Morse sequence and Cambridge University Press · See more »

Chess

Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid.

New!!: Thue–Morse sequence and Chess · See more »

Combinatorics on words

Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages.

New!!: Thue–Morse sequence and Combinatorics on words · See more »

Complex Systems (journal)

Complex Systems is a quarterly peer-reviewed open access scientific journal covering subjects ranging across a number of scientific and engineering fields, including computational biology, computer science, mathematics, and physics.

New!!: Thue–Morse sequence and Complex Systems (journal) · See more »

Concentration

In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture.

New!!: Thue–Morse sequence and Concentration · See more »

Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

New!!: Thue–Morse sequence and Continuous function · See more »

Critical exponent of a word

In mathematics and computer science, the critical exponent of a finite or infinite sequence of symbols over a finite alphabet describes the largest number of times a contiguous subsequence can be repeated.

New!!: Thue–Morse sequence and Critical exponent of a word · See more »

Degree of a polynomial

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

New!!: Thue–Morse sequence and Degree of a polynomial · See more »

Dejean's theorem

Dejean's theorem (formerly Dejean's conjecture) is a statement about repetitions in infinite strings of symbols.

New!!: Thue–Morse sequence and Dejean's theorem · See more »

Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

New!!: Thue–Morse sequence and Derivative · See more »

Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

New!!: Thue–Morse sequence and Differential geometry · See more »

Discrete Applied Mathematics

Discrete Applied Mathematics is a peer-reviewed academic journal in mathematics, published by Elsevier.

New!!: Thue–Morse sequence and Discrete Applied Mathematics · See more »

Disjoint sets

In mathematics, two sets are said to be disjoint sets if they have no element in common.

New!!: Thue–Morse sequence and Disjoint sets · See more »

Ethiopian cuisine

Ethiopian cuisine (የኢትዮጵያ ምግብ) characteristically consists of vegetable and often very spicy meat dishes.

New!!: Thue–Morse sequence and Ethiopian cuisine · See more »

Evil number

In number theory, an evil number is a non-negative integer that has an even number of 1s in its binary expansion.

New!!: Thue–Morse sequence and Evil number · See more »

Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

New!!: Thue–Morse sequence and Exclusive or · See more »

Fabius function

In mathematics, the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by.

New!!: Thue–Morse sequence and Fabius function · See more »

Fair division

Fair division is the problem of dividing a set of goods or resources between several people who have an entitlement to them, such that each person receives his/her due share.

New!!: Thue–Morse sequence and Fair division · See more »

Fixed point (mathematics)

In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.

New!!: Thue–Morse sequence and Fixed point (mathematics) · See more »

Flat function

In mathematics, especially real analysis, a flat function is a smooth function ƒ: ℝ → ℝ all of whose derivatives vanish at a given point x0 ∈.

New!!: Thue–Morse sequence and Flat function · See more »

Formal power series

In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.

New!!: Thue–Morse sequence and Formal power series · See more »

Fractals (journal)

Fractals is a peer-reviewed scientific journal devoted to explaining complex phenomena using fractal geometry and scaling.

New!!: Thue–Morse sequence and Fractals (journal) · See more »

Free monoid

In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element.

New!!: Thue–Morse sequence and Free monoid · See more »

Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

New!!: Thue–Morse sequence and Function (mathematics) · See more »

Gesine Reinert

Gesine Reinert is a University Professor in Statistics at the University of Oxford.

New!!: Thue–Morse sequence and Gesine Reinert · See more »

GF(2)

GF(2) (also F2, Z/2Z or Z2) is the '''G'''alois '''f'''ield of two elements.

New!!: Thue–Morse sequence and GF(2) · See more »

Gradient

In mathematics, the gradient is a multi-variable generalization of the derivative.

New!!: Thue–Morse sequence and Gradient · See more »

Grandmaster (chess)

The title Grandmaster (GM) is awarded to chess players by the world chess organization FIDE.

New!!: Thue–Morse sequence and Grandmaster (chess) · See more »

Hamming weight

The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used.

New!!: Thue–Morse sequence and Hamming weight · See more »

Hans Rademacher

Hans Adolph Rademacher (3 April 1892, Wandsbeck, now Hamburg-Wandsbek – 7 February 1969, Haverford, Pennsylvania, USA) was a German-born American mathematician, known for work in mathematical analysis and number theory.

New!!: Thue–Morse sequence and Hans Rademacher · See more »

John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

New!!: Thue–Morse sequence and John Horton Conway · See more »

Kayles

In combinatorial game theory, Kayles is a simple impartial game.

New!!: Thue–Morse sequence and Kayles · See more »

Koch snowflake

The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described.

New!!: Thue–Morse sequence and Koch snowflake · See more »

L (complexity)

In computational complexity theory, L (also known as LSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space.

New!!: Thue–Morse sequence and L (complexity) · See more »

L-system

An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar.

New!!: Thue–Morse sequence and L-system · See more »

List of Latin phrases (E)

Additional sources.

New!!: Thue–Morse sequence and List of Latin phrases (E) · See more »

Marston Morse

Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory.

New!!: Thue–Morse sequence and Marston Morse · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Thue–Morse sequence and Mathematics · See more »

Max Euwe

Machgielis "Max" Euwe, PhD (May 20, 1901 – November 26, 1981) was a Dutch chess Grandmaster, mathematician, author, and chess administrator.

New!!: Thue–Morse sequence and Max Euwe · See more »

Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

New!!: Thue–Morse sequence and Monotonic function · See more »

Morphic word

In mathematics and computer science, a morphic word or substitutive word is an infinite sequence of symbols which is constructed from a particular class of endomorphism of a free monoid.

New!!: Thue–Morse sequence and Morphic word · See more »

Nimber

In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim.

New!!: Thue–Morse sequence and Nimber · See more »

Nonlinear system

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.

New!!: Thue–Morse sequence and Nonlinear system · See more »

Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

New!!: Thue–Morse sequence and Number theory · See more »

Odious number

In number theory, an odious number is a non-negative number that has an odd number of 1s in its binary expansion.

New!!: Thue–Morse sequence and Odious number · See more »

Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

New!!: Thue–Morse sequence and Orthogonality · See more »

Palindromic number

A palindromic number or numeral palindrome is a number that remains the same when its digits are reversed.

New!!: Thue–Morse sequence and Palindromic number · See more »

Partition of a set

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

New!!: Thue–Morse sequence and Partition of a set · See more »

Periodic sequence

In mathematics, a periodic sequence (sometimes called a cycle) is a sequence for which the same terms are repeated over and over: The number p of repeated terms is called the period (period).

New!!: Thue–Morse sequence and Periodic sequence · See more »

Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

New!!: Thue–Morse sequence and Polynomial · See more »

Port and starboard

Port and starboard are nautical and aeronautical terms for left and right, respectively.

New!!: Thue–Morse sequence and Port and starboard · See more »

Prouhet–Tarry–Escott problem

In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials are all equal.

New!!: Thue–Morse sequence and Prouhet–Tarry–Escott problem · See more »

Prouhet–Thue–Morse constant

In mathematics, the Prouhet–Thue–Morse constant, named for Eugène Prouhet, Axel Thue, and Marston Morse, is the number—denoted by \tau—whose binary expansion.01101001100101101001011001101001...

New!!: Thue–Morse sequence and Prouhet–Thue–Morse constant · See more »

Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

New!!: Thue–Morse sequence and Recurrence relation · See more »

Recurrent word

In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely often.

New!!: Thue–Morse sequence and Recurrent word · See more »

Recursion

Recursion occurs when a thing is defined in terms of itself or of its type.

New!!: Thue–Morse sequence and Recursion · See more »

Rowing (sport)

Rowing, often referred to as crew in the United States, is a sport whose origins reach back to Ancient Egyptian times.

New!!: Thue–Morse sequence and Rowing (sport) · See more »

Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

New!!: Thue–Morse sequence and Set (mathematics) · See more »

Sprague–Grundy theorem

In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a nimber.

New!!: Thue–Morse sequence and Sprague–Grundy theorem · See more »

Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

New!!: Thue–Morse sequence and Springer Science+Business Media · See more »

Square-free word

In combinatorics, a square-free word is a word (a sequence of characters) that does not contain any subword twice in a row.

New!!: Thue–Morse sequence and Square-free word · See more »

Step function

In mathematics, a function on the real numbers is called a step function (or staircase function) if it can be written as a finite linear combination of indicator functions of intervals.

New!!: Thue–Morse sequence and Step function · See more »

Steven Brams

Steven J. Brams (born November 28, 1940 in Concord, New Hampshire) is an American game theorist and political scientist at the New York University Department of Politics.

New!!: Thue–Morse sequence and Steven Brams · See more »

Streetball

Streetball or street basketball is a variation of basketball typically played on outdoor courts, featuring significantly less formal structure and enforcement of the game's rules.

New!!: Thue–Morse sequence and Streetball · See more »

Teacher

A teacher (also called a school teacher or, in some contexts, an educator) is a person who helps others to acquire knowledge, competences or values.

New!!: Thue–Morse sequence and Teacher · See more »

Threefold repetition

In chess and some other abstract strategy games, the threefold repetition rule (also known as repetition of position) states that a player can claim a draw if the same position occurs three times, or will occur after their next move, with the same player to move.

New!!: Thue–Morse sequence and Threefold repetition · See more »

Turtle graphics

In computer graphics, turtle graphics are vector graphics using a relative cursor (the "turtle") upon a Cartesian plane.

New!!: Thue–Morse sequence and Turtle graphics · See more »

Walsh function

In mathematics, more specifically in harmonic analysis, Walsh functions form a complete orthogonal set of functions that can be used to represent any discrete function—just like trigonometric functions can be used to represent any continuous function in Fourier analysis.

New!!: Thue–Morse sequence and Walsh function · See more »

Wojciech Szpankowski

Wojciech Szpankowski is the Saul Rosen Professor of Computer Science at the Purdue University.

New!!: Thue–Morse sequence and Wojciech Szpankowski · See more »

Redirects here:

Generalised Morse Sequence, Generalised Morse sequence, Generalised morse sequence, Generalized Morse sequence, Morse sequence, Morse-Thue sequence, PTM sequence, Prouhet-Thue-Morse sequence, Prouhet-Thue-Morse system, Prouhet–Thue–Morse sequence, Thue sequence, Thue-Morse Sequence, Thue-Morse sequence.

References

[1] https://en.wikipedia.org/wiki/Thue–Morse_sequence

OutgoingIncoming
Hey! We are on Facebook now! »