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Alternating polynomial
About: Alternating polynomial is a research topic. Over the lifetime, 2283 publications have been published within this topic receiving 33334 citations.
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TL;DR: The method of showing density ymlds the result that if P ~ NP then there are members of NP -P that are not polynomml complete is shown, which means there is a strictly ascending sequence with a minimal pair of upper bounds to the sequence.
Abstract: Two notions of polynomml time reduclbihty, denoted here by ~ T e and <.~P, were defined by Cook and Karp, respectively The abstract propertms of these two relatmns on the domain of computable sets are investigated. Both relations prove to be dense and to have minimal pairs. Further , there is a strictly ascending sequence with a minimal pair of upper bounds to the sequence. Our method of showing density ymlds the result that if P ~ NP then there are members of NP -P that are not polynomml complete
783 citations
01 Jan 1980
TL;DR: Polynomial Representations of GLn(K): The Schur algebra as mentioned in this paper, Weights and Characters., The modules D?K., The Carter-Lusztig modules V?,K., Representation theory of the symmetric group
Abstract: Polynomial Representations of GLn(K): The Schur algebra.- Weights and Characters.- The modules D?,K.- The Carter-Lusztig modules V?,K.- Representation theory of the symmetric group.
755 citations
TL;DR: In this paper, a generalization of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures is presented.
Abstract: A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement these with illustrative examples.
469 citations
01 Nov 2005
TL;DR: Polynomial identities and PI-algebras $S_n$-representations Group gradings and group actions Codimension and colength growth Matrix invariants and central polynomials The PI-exponent of an algebra Polynomial growth and low PIexponent Classifying minimal varieties Computing the exponent of a polynomial.
Abstract: Polynomial identities and PI-algebras $S_n$-representations Group gradings and group actions Codimension and colength growth Matrix invariants and central polynomials The PI-exponent of an algebra Polynomial growth and low PI-exponent Classifying minimal varieties Computing the exponent of a polynomial $G$-identities and $G\wr S_n$-action Superalgebras, *-algebras and codimension growth Lie algebras and nonassociative algebras The generalized-six-square theorem Bibliography Index.
433 citations
TL;DR: In this article, it was shown that the special linear group of degree not less than three over the polynomial ring over a field is generated by the elementary matrices, and that the general linear group over the Laurent ring is also composed of the same matrices.
Abstract: It is proved that the special linear group of degree not less than three over the polynomial ring over a field is generated by the elementary matrices. Other results are obtained that relate to the structure of the special linear group and stabilization of the general linear group over arbitrary polynomial and Laurent rings.Bibliography: 9 titles.
381 citations