We give a basis for the space spanned by the sum ŝλ of the lowest degree terms in the expansion of the Schur symmetric functions sλ in terms of the power sum symmetric functions pμ, where deg(pi) = 1. These lowest degree terms correspond to minimal border strip tableaux of λ. The dimension of the space spanned by ŝλ, where λ is a partition of n, is equal to the number of partitions of n into pa...

For any set representation (permutation representation) of the symmetric group Sn, we give combinatorial interpretation for coefficients of its Frobenius character expanded in the basis of monomial symmetric functions.

Let P be the orthogonal projection from L(B, dv) onto the Bergman space La(B, dv) of the unit ball in C . In this paper we characterize the membership of commutators of the form [Mf , P ] in the norm ideal CΦ, where the symmetric gauge function Φ is allowed to be arbitrary.

By the fundamental theorem of symmetric polynomials, if P ∈ Q[X1, . . . , Xn] is symmetric, then it can be written P = Q(σ1, . . . , σn), where σ1, . . . , σn are the elementary symmetric polynomials in n variables, and Q is in Q[S1, . . . , Sn]. We investigate the complexity properties of this construction in the straight-line program model, showing that the complexity of evaluation of Q depen...

‎in this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎the proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the newton equation system‎, ‎by using an inexact newton direction‎. ‎furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

The hit problem for a cohomology module over the Steenrod algebra A asks for a minimal set of A-generators for the module. In this paper we consider the symmetric algebras over the field Fp, for p an arbitrary prime, and treat the equivalent problem of determining the set of A∗-primitive elements in their duals. We produce a method for generating new primitives from known ones via a new action ...

We study the explicit formula of Lusztig’s integral forms of the level one quantum affine algebra Uq(ŝl2) in the endomorphism ring of symmetric functions in infinitely many variables tensored with the group algebra of Z. Schur functions are realized as certain orthonormal basis vectors in the vertex representation associated to the standard Heisenberg algebra. In this picture the Littlewood-Ric...

Abstract. In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and power sum symmetric polynomials. We investigate properties of these families and focus on constructing their rational roots under a product induce...