Oct 19, 2010 - many areas of mathematics such as numerical analysis, differential ... 2000 Mathematics Subject Classification: 15A24, 16E40 (primary), 16E99 (secondary). ... Let G be an undirected graph with n vertices labeled by the set {1,2,...,n}.
In this work we are going to extend the proof of Newton's theorem of symmetric ..... [2] D. A.Cox, Galois Theory, John Wiley and Sons, INC., New Jersey, 2004.
we apply these results to some problems in number theory on sums of products of ..... Note that if the number of indeterminates xi is Lâ1 then the right side in (6).
labeled by the compact manifold Sj of all tripotents of equal rank j . The .... [0, 1.10], Td(£) ü the Todd class of the "Peirce %-bundle" E = {Z1/2{e)) over Si and hi,...
Apr 2, 2008 - AC] 2 Apr 2008. REGULAR SEQUENCES OF SYMMETRIC POLYNOMIALS. ALDO CONCA, CHRISTIAN KRATTENTHALERâ , JUNZO ...
Jul 10, 2015 - orthogonal polynomials satisfying the Leonard duality [2]; see [3] for an overview. ..... [20] G. Andrews, R. Askey, R. Roy, Special functions, Vol.
Nov 23, 2012 - The set consists of four polynomials of degrees 2,6,8, and 12, for ... exception from this conclusion are entanglement measures that are defined in terms of .... Thus if F(x0,x1,x2,x3) is a polynomial in the indeterminates xj then ...
Oct 7, 2013 - arXiv:1310.1658v1 [math.NT] 7 Oct 2013. SYMMETRIC IDENTITIES OF THE q-EULER POLYNOMIALS. DAE SAN KIM AND TAEKYUN KIM.
Apr 8, 2016 - It is natural to try to generalize this method to four and more variables, ... terms of a given degree is itself a symmetric polynomial and if we can ...
Jul 1, 2016 - French mathematicians in honor of the Brazilian computer scientist Imre Simon [14], one of the pioneers in min-plus algebra. It builds on the ...
{T} of real symmetric Toeplitz matrices generated by a rational function f(z) with real coefficients such ... no zeros in |z| < 1, C(z) = B(2)B(1/2), and. B(z) = E b,7",.
Karatsuba and Ofman [KO63] and the matrix-multiplication algorithm of Strassen [Str69]. A new field with surprising algorithms is quantum computing. The most ...
In [2] we prove. THEOREM 1. Let G be an extension of the local field F. Let X and Y be nonsingular symmetric matrices over G such that dim X â dim Y and.
Nov 2, 2018 - Given a graph r with vertex set V = {v1,..., vn}, the adjacency matrix of r is ... ordering of the vertices and is denoted hereafter by Ïr(x).
Nov 29, 2018 - (9). Here Bn,Ï := Bn,Ï(0) are the generalized Bernoulli numbers attached to Ï. From Equation (9), we have. (see, e.g., [16]). â«. X Ï(x)xndx = Bn,Ï.
results generalize for other non-prime power composite moduli as well. The proof uses perfect hashing functions and the famous BBR-polynomial of Barrington, ...
Apr 15, 2016 - CO] 15 Apr 2016 ..... other types, defined via crystal operators, see for example [PH15]. ..... Proposition 15 (Basement permuting operators).
Jun 7, 2006 - symmetric functions and obtain Vi`ete formula and decompositions of dif- ferential ..... equation relating Vandermonde and Wronskian matrices.
Jan 26, 2018 - Sara Kališnik. Max Planck Institute for Mathematics in the Sciences, [email protected]. Wesleyan University, skalisnikver@wesleyan.
Mar 19, 2008 - a Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK b Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA ...... Technical Mathematics and Informatics No.
Jun 20, 2014 - (5). However, based on the Hirota -operators, Professor Ma put forward ..... The authors declare that there is no conflict of interests regarding ...
Jun 25, 2011 - Many authors have considered the problem of extension and lifting of operators. [19, 20 ... exact sequences F-split while, as it will be clear after definition 2, not all exact ..... Let j : F(V,Y ) â A(V,Y ) denote the canonical emb
May 30, 2017 - Seo gave the answer to a problem suggested by Stanley by ..... all these determinants, we can guarantee to have a correct reduction.
vehicle for exploring many integer sequences, and can provide insight into ...... [8] N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, Notices of ...
I would like to thank Boris Feigin, Eugene Gorsky, Andrei Okounkov, Alexander. Tsymbaliuk for their patience in explaining many of these things to me, and for.
OPERATORS ON SYMMETRIC POLYNOMIALS ANDREI NEGUT
1. Introduction The purpose of this note is to give a brief survey of certain operators on symmetric polynomials. There are many ways to write them, but the way we will mostly focus on was defined in [3] in terms of the shuffle algebra. This algebra was introduced quite generally in [4], though we will only need a particular case of their construction, which we will recall in Subsection 2.5. The shuffle algebra (more precisely, its Drinfeld double) acts on the well-known ring of symmetric polynomials: Λ = Q(q, t)[x1 , x2 , ...]Sym This action includes certain well-known operators on this vector space, such as: • the operator of multiplication by f , for any f ∈ Λ, • the Macdonald eigenoperator Dg for any g ∈ Λ, given by: Dg (Pλ ) = g [(1 − q)(1 − t) · weights outside the partition λ] · Pλ
(1.1)
1
Throughout this note, Pλ will denote the modified Macdonald polynomials, which are orthogonal with respect to the inner product (2.3). One of the new formulas we present in this paper expresses Dg as a certain vertex operator in the spirit of [3], for a wide class of symmetric polynomials g called rim-hook (or ribbon) skew Schur functions. This uses the results of [6] about the structure of the shuffle algebra. In particular, we have: Theorem 1.2. The Macdonald eigenoperator Dn = Dpn is given by: P n zn (qt)n−i Q zi Z ω i=1 i
