For the orthogonal polynomials in several variables, see Hall–Littlewood polynomials.
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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a Littlewoodpolynomial is a polynomial all of whose coefficients are +1 or −1. Littlewood's problem asks how large the values of such a polynomial must...
combination of Schur polynomials with non-negative integral coefficients; the values of these coefficients is given combinatorially by the Littlewood–Richardson...
theorem Littlewood conjecture LittlewoodpolynomialLittlewood's three principles of real analysis Littlewood's Tauberian theorem Littlewood's 4/3 inequality...
construct an explicit β such that (α,β) satisfies the conjecture. Littlewoodpolynomial J.W.S. Cassels; H.P.F. Swinnerton-Dyer (1955-06-23). "On the product...
orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...
subgroups lemma Hall algebra, and Hall polynomials Hall subgroup Hall–Higman theorem Hall–Littlewoodpolynomial Hall's universal group Hall's marriage...
both even, the polynomial produces only even values, and is therefore composite except possibly for the value 2. Hardy and Littlewood assert that, apart...
Sahasrabudhe's work covers many topics such as Littlewood problems on polynomials, probability and geometry of polynomials, arithmetic Ramsey theory, Erdős covering...
other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewoodpolynomials and Askey–Wilson polynomials, which in turn include most...
one-variable specializations of the Kostka polynomials can be used to relate Hall-Littlewoodpolynomials Pμ to Schur polynomials sλ: s λ ( x 1 , … , x n ) = ∑ μ...
Szeged Died: John Littlewood, 92, British mathematician known for the Littlewood conjecture, the Littlewoodpolynomial, Littlewood–Paley theory, the two...
Hall: Hall polynomial, Hall–Littlewoodpolynomial Hermann Hankel: Hankel function Heine: Heine functions Charles Hermite: Hermite polynomials Karl L. W...
In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties. They...
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...
Number theorists have worked on polynomials with restricted coefficients over the years. For instance, Littlewoodpolynomials have coefficients ±1 when expressed...
expand Macdonald polynomials in terms of LLT polynomials. Ian Grojnowski and Mark Haiman proved a positivity conjecture for LLT polynomials that combined...
}\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...
Press. doi:10.1017/CBO9780511546556. ISBN 9780511546556. Littlewood, D. E. (1936), "Polynomial concomitants and invariant matrices", J. London Math. Soc...