Results 231 to 240 of about 1,007,951 (256)

A note on identities for elementary symmetric and power sum polynomials

Discrete Mathematics, Algorithms and Applications, 2018
We provide a lightweight algorithm to express each of the elementary symmetric polynomials as a linear combination of (products of) power sum symmetric polynomials and, also, the power sums purely in terms of the elementary symmetric polynomials. Our method does not use Newton’s identities, which give such relations only implicitly.
Kent D. Boklan
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On the elementary symmetric polynomials of independent random variables

Acta Mathematica Hungarica, 1976
G Halasz
exaly   +3 more sources

On estimation with elementary symmetric polynomials

rose, 1998
Let \(X_1,\dots ,X_n\) be a random sample from a distribution function which belongs to a family \(F\) with \(E X_1=\theta \in \Theta\). Let \[ S_n^{(k)}=\left(C_n^k\right)^{-1}\sum_{1\leq{i_1}\leq\dots\leq{i_k}\leq n} X_{i_1}\cdots X_{i_k} \] \[ \; \] be an estimate of \(\theta^k\) and let \(S_m=\sum_{k=0}^m a_k S_n^{(k)}\) be an estimate of \(g_m ...
Rempala, Grzegorz, Székely, Gábor
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A POLYNOMIAL WITH COEFFICIENTS IN CERTAIN ELEMENTARY SYMMETRIC POLYNOMIALS

JP Journal of Algebra, Number Theory and Applications, 2017
Summary: Let \(\overline{M}_n\) be the configuration space of equilateral planar \(n\)-gons modulo isometry group. For odd \(n\), the mod 2 cohomology ring \(H^\ast(\overline{M}_n;\mathbb{Z}_2)\) has the form \[ H^\ast(\overline{M}_n;\mathbb{Z}_2)=\mathbb{Z}_2[R,V_1,\ldots,V_{n-1}]/\mathcal{J}, \] where the ideal \(\mathcal{J}\) is generated by three ...
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Elementary Symmetric Polynomials in Random Variables

Acta Applicandae Mathematicae, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Shifted Partial Derivative Complexity of Elementary Symmetric Polynomials

2015
We continue the study of the shifted partial derivative measure, introduced by Kayal (ECCC 2012), which has been used to prove many strong depth-4 circuit lower bounds starting from the work of Kayal, and that of Gupta et al. (CCC 2013).
Hervé Fournier, Nutan Limaye, Meena Mahajan, Srikanth Srinivasan 0001   +3 more
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Almost sure behavior of elementary symmetric polynomials

rose, 2000
The problem of asymptotic behavior of elementary (random) symmetric polynomials (ESPs) was considered by many authors. Whereas the weak convergence properties of ESPs were intensely studied, it seems that the problem of the almost sure behavior did not receive equal attention. The main result in this direction was obtained by \textit{G.
Rempala, Grzegorz, Gupta, Arjun
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Concentration for limited independence via inequalities for the elementary symmetric polynomials

Theory Comput., 2020
Summary: We study the extent of independence needed to approximate the product of bounded random variables in expectation. This natural question has applications in pseudorandomness and min-wise independent hashing. For random variables with absolute value bounded by \(1\), we give an error bound of the form \(\sigma^{\Omega(k)}\) when the input is \(k\
Parikshit Gopalan, Amir Yehudayoff
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Differential equations for the elementary 3-symmetric Chebyshev polynomials

Journal of Mathematical Sciences, 2013
This is a part of the authors' study of the polynomials \(\psi_n(x)\) satisfying the three-term recurrence relation \(x\psi_n(x)=\psi_{n+1}(x)+a_n\psi_n(x)+\psi_{n-1}(x)\) with the periodic coefficient \(a_n=a_{n+3}\) and the initial conditions \(\psi_{-1}(x)\equiv0\), \(\psi_0(x)\equiv1\). The polynomials corresponding to the triplet \(\{a_0,a_1,a_2\}=
Borzov, V. V., Damaskinsky, E. V.
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Elementary Symmetric Polynomial Inequalities for Centered Vectors and Matrices

We prove new inequalities for elementary symmetric polynomials (ESPs) for vectors that sum to zero, and for square matrices with zero row and column sums. We apply these results to obtain a unified upper bound on the mean-field approximation guarantee for permutation mixtures, as well as a sharp $χ^2$ version of the de Finetti theorem for finite ...
Han, Yanjun, Niles-Weed, Jonathan
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