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Littlewood polynomial information


Roots of all the Littlewood polynomials of degree 15.

In mathematics, a Littlewood polynomial is a polynomial all of whose coefficients are +1 or −1. Littlewood's problem asks how large the values of such a polynomial must be on the unit circle in the complex plane. The answer to this would yield information about the autocorrelation of binary sequences. They are named for J. E. Littlewood who studied them in the 1950s.

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Littlewood polynomial

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a Littlewood polynomial is a polynomial all of whose coefficients are +1 or −1. Littlewood's problem asks how large the values of such a polynomial must...

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List of polynomial topics

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Koornwinder polynomials Kostka polynomial Kravchuk polynomials Laguerre polynomials Laurent polynomial Linearised polynomial Littlewood polynomial Legendre...

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Schur polynomial

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combination of Schur polynomials with non-negative integral coefficients; the values of these coefficients is given combinatorially by the Littlewood–Richardson...

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John Edensor Littlewood

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theorem Littlewood conjecture Littlewood polynomial Littlewood's three principles of real analysis Littlewood's Tauberian theorem Littlewood's 4/3 inequality...

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Littlewood conjecture

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construct an explicit β such that (α,β) satisfies the conjecture. Littlewood polynomial J.W.S. Cassels; H.P.F. Swinnerton-Dyer (1955-06-23). "On the product...

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Orthogonal polynomials

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orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...

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Philip Hall

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subgroups lemma Hall algebra, and Hall polynomials Hall subgroup Hall–Higman theorem Hall–Littlewood polynomial Hall's universal group Hall's marriage...

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Dragon curve

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set of Littlewood polynomials can be arrived at by such iterated applications of a set of functions. A Littlewood polynomial is a polynomial: p ( x )...

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Ulam spiral

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both even, the polynomial produces only even values, and is therefore composite except possibly for the value 2. Hardy and Littlewood assert that, apart...

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Julian Sahasrabudhe

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Sahasrabudhe's work covers many topics such as Littlewood problems on polynomials, probability and geometry of polynomials, arithmetic Ramsey theory, Erdős covering...

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Macdonald polynomials

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other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include most...

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Kostka polynomial

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one-variable specializations of the Kostka polynomials can be used to relate Hall-Littlewood polynomials Pμ to Schur polynomials sλ: s λ ( x 1 , … , x n ) = ∑ μ...

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September 1977

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Szeged Died: John Littlewood, 92, British mathematician known for the Littlewood conjecture, the Littlewood polynomial, Littlewood–Paley theory, the two...

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List of eponyms of special functions

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Hall: Hall polynomial, Hall–Littlewood polynomial Hermann Hankel: Hankel function Heine: Heine functions Charles Hermite: Hermite polynomials Karl L. W...

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Schubert polynomial

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In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties. They...

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Big O notation

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sense "is not an o of") was introduced in 1914 by Hardy and Littlewood. Hardy and Littlewood also introduced in 1916 the symbols Ω R {\displaystyle \Omega...

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Bohemian matrices

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Number theorists have worked on polynomials with restricted coefficients over the years. For instance, Littlewood polynomials have coefficients ±1 when expressed...

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LLT polynomial

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expand Macdonald polynomials in terms of LLT polynomials. Ian Grojnowski and Mark Haiman proved a positivity conjecture for LLT polynomials that combined...

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Riemann hypothesis

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}\right)} for every positive ε is equivalent to the Riemann hypothesis (J. E. Littlewood, 1912; see for instance: paragraph 14.25 in Titchmarsh (1986)). The determinant...

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Shapiro polynomials

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n/2\rfloor -1}.\,} Littlewood polynomials John Brillhart and L. Carlitz (May 1970). "Note on the Shapiro polynomials". Proceedings of the American...

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Plethysm

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Press. doi:10.1017/CBO9780511546556. ISBN 9780511546556. Littlewood, D. E. (1936), "Polynomial concomitants and invariant matrices", J. London Math. Soc...

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