Results 11 to 20 of about 1,894,941 (290)
Definability by constant-depth polynomial-size circuits [PDF]
Information and Control, 1986 A class \(\Sigma\) of \(\sigma\)-structures is called circuit definable if there is a constant-depth, polynomial-size bounded sequence \(C_1, \ldots, C_n,\ldots\) of circuits, where each \(C_n\) is symmetric and accepts a structure \(S\) on the universe \(U_n=\{0,\ldots, n-1\}\) iff \(S\in \Sigma\).
Larry Denenberg +2 more
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Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width [PDF]
, 1998 It is known that evaluating the Tutte polynomial, $T(G; x, y)$, of a graph, $G$, is $\#$P-hard at all but eight specific points and one specific curve of the $(x, y)$-plane.
Noble, S D
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Estimates of the asymptotic Nikolskii constants for spherical polynomials [PDF]
Journal of Complexity, 2021 Let $Π_n^d$ denote the space of spherical polynomials of degree at most $n$ on the unit sphere $\mathbb{S}^d\subset \mathbb{R}^{d+1}$ that is equipped with the surface Lebesgue measure $dσ$ normalized by $\int_{\mathbb{S}^d} \, dσ(x)=1$. This paper establishes a close connection between the asymptotic Nikolskii constant, $$ \mathcal{L}^\ast(d):=\lim_{n\
Feng Dai +2 more
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Asymptotics of Polynomial Interpolation and the Bernstein Constants [PDF]
Results in Mathematics, 2021 AbstractIt is well known that the interpolation error for $$\left| x\right| ^{\alpha },\alpha >0$$ x α , α > 0
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Learning Read-Constant Polynomials of Constant Degree Modulo Composites [PDF]
Theory of Computing Systems, 2011 Peer ...
Arkadev Chattopadhyay +3 more
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Constant term identities and Poincaré polynomials [PDF]
Transactions of the American Mathematical Society, 2015 In 1982 Macdonald published his now famous constant term conjectures for classical root systems. This paper begins with the almost trivial observation that Macdonald’s constant term identities admit an extra set of free parameters, thereby linking them to Poincaré polynomials.
Károlyi, Gyula +2 more
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Decomposition of differential polynomials with constant coefficients [PDF]
Proceedings of the 2004 international symposium on Symbolic and algebraic computation, 2004 In this paper, we present an algorithm to decompose differential polynomials in one variable and with rational number as coefficients. Besides arithmetic operations, the algorithm needs only factorization of multi-variable polynomials and solution of linear equation systems. Experimental results show that our method is quite efficient.
Xiao-Shan Gao, Mingbo Zhang
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Contributions to polynomial system solving: Recurrences and Gröbner bases
, 2023 This habilitation thesis deals with polynomial system solving through Gröbner bases computations. It focuses on the link between multivariate polynomials and linear recurrence relations satisfied by a multi-indexed sequence for computing Gröbner ...
Berthomieu, Jérémy
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Exploiting constant trace property in large-scale polynomial optimization
, 2022 43 pages, 6 algorithms, 23 tablesInternational audienceWe prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant ...
Mai, Ngoc Hoang Anh +7 more
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Constant Terms of Near-Dyson Polynomials [PDF]
The Electronic Journal of Combinatorics, 2018 We formulate and prove a formula for the constant term for a certain class of Laurent polynomials, which include the Dyson conjecture and its generalizations by Bressoud and Goulden. Our method is explicit Combinatorial Nullstellensatz.
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