نتایج جستجو برای: relative symmetric polynomials

تعداد نتایج: 501696  

Journal: :J. Comput. Syst. Sci. 2001
Amir Shpilka

In this paper we introduce a new model for computing polynomials a depth 2 circuit with a symmetric gate at the top and plus gates at the bottom, i.e the circuit computes a symmetric function in linear functions Sd m(`1; `2; :::; `m) (Sd m is the d’th elementary symmetric polynomial in m variables, and the `i’s are linear functions). We refer to this model as the symmetric model. This new model...

Journal: :SIAM J. Matrix Analysis Applications 2006
Nicholas J. Higham D. Steven Mackey Niloufer Mackey Françoise Tisseur

A standard way of treating the polynomial eigenvalue problem P (λ)x = 0 is to convert it into an equivalent matrix pencil—a process known as linearization. Two vector spaces of pencils L1(P ) and L2(P ), and their intersection DL(P ), have recently been defined and studied by Mackey, Mackey, Mehl, and Mehrmann. The aim of our work is to gain new insight into these spaces and the extent to which...

Journal: :Symmetry 2023

Some new formulas related to the well-known symmetric Lucas polynomials are primary focus of this article. Different approaches used for establishing these formulas. A matrix approach is followed in order obtain some fundamental properties. Particularly, recurrence relations and determinant forms determined by suitable Hessenberg matrices. Conjugate generating functions derived examined. Severa...

Journal: :Electronic Colloquium on Computational Complexity (ECCC) 2014
Parikshit Gopalan Amir Yehudayoff

This paper studies the elementary symmetric polynomials Sk(x) for x ∈ Rn. We show that if |Sk(x)|, |Sk+1(x)| are small for some k > 0 then |S`(x)| is also small for all ` > k. We use this to prove probability tail bounds for the symmetric polynomials when the inputs are only t-wise independent, which may be useful in the context of derandomization. We also provide examples of t-wise independent...

Journal: :Graphs and Combinatorics 2010
Yong Zhang Zhi-Wei Sun Hao Pan

In this paper we establish two symmetric identities on sums of products of Euler polynomials.

2008
ALDO CONCA CHRISTIAN KRATTENTHALER JUNZO WATANABE

A set of n homogeneous polynomials in n variables is a regular sequence if the associated polynomial system has only the obvious solution (0, 0, . . . , 0). Denote by pk(n) the power sum symmetric polynomial in n variables x k 1 +x 2 + · · ·+xk n . The interpretation of the q-analogue of the binomial coefficient as Hilbert function leads us to discover that n consecutive power sums in n variabl...

2011
Lenny Tevlin

Noncommutative symmetric functions have many properties analogous to those of classical (commutative) symmetric functions. For instance, ribbon Schur functions (analogs of the classical Schur basis) expand positively in noncommutative monomial basis. More of the classical properties extend to noncommutative setting as I will demonstrate introducing a new family of noncommutative symmetric funct...

Journal: :Foundations of Computational Mathematics 2010
J. M. Landsberg Zach Teitler

Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We provide improved lower bounds for the rank of a symmetric tensor (i.e., a homogeneous polynomial) obtained by considering the singularities of the hypersurface defined by the polynomial. We obtain normal forms for po...

Journal: :Electr. J. Comb. 2001
Leigh Roberts

Recently Lapointe et. al. [3] have expressed Jack Polynomials as determinants in monomial symmetric functions mλ. We express these polynomials as determinants in elementary symmetric functions eλ, showing a fundamental symmetry between these two expansions. Moreover, both expansions are obtained indifferently by applying the Calogero-Sutherland operator in physics or quasi Laplace Beltrami oper...

2017
Ewin Tang

This behavior has been seen in some notable cases. Kirillov [3] shows that elementary symmetric polynomials in noncommuting variables commute (and, in some cases, all Schur functions) when elementary symmetric polynomials of degree at most three commute when restricted to at most three of the variables. Generalizing this, Blasiak and Fomin [1] give a wider theory for rules of three of generatin...

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