منابع مشابه
The Coefficient Coalgebra of a Symmetrized Tensor Space
The coefficient coalgebra of r-fold tensor space and its dual, the Schur algebra, are generalized in such a way that the role of the symmetric group Σr is played by an arbitrary subgroup of Σr. The dimension of the coefficient coalgebra of a symmetrized tensor space is computed and the dual of this coalgebra is shown to be isomorphic to the analog of the Schur algebra. 0. Introduction Let K be ...
متن کاملA remark on asymptotic enumeration of highest weights in tensor powers of a representation
We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...
متن کاملDerivatives of tensor powers and their norms
The norm of the mth derivative of the map that takes an operator to its kth antisymmetric tensor power is evaluated. The case m = 1 has been studied earlier by Bhatia and Friedland [R. Bhatia and S. Friedland. Variation of Grassman powers and spectra. Linear Algebra and its Applications, 40:1–18, 1981]. For this purpose a multilinear version of a theorem of Russo and Dye is proved: it is shown ...
متن کاملOn Tensor Powers of Integer Programs
We de ne a natural product on integer programming problems with nonnegative coe cients. Hypergraph covering problems are a special case of such integer programs, and the product we de ne is a generalization of the usual hypergraph product. The main theorem of this paper gives a su cient condition under which the solution to the nth power of an integer program is asymptotically as good as the so...
متن کاملIndependent sets in tensor graph powers
The tensor product of two graphs, G and H, has a vertex set V (G) × V (H) and an edge between (u, v) and (u′, v′) iff both uu′ ∈ E(G) and vv′ ∈ E(H). Let A(G) denote the limit of the independence ratios of tensor powers of G, limα(G)/|V (G)|. This parameter was introduced in [5], where it was shown that A(G) is lower bounded by the vertex expansion ratio of independent sets of G. In this note w...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2001
ISSN: 0747-7171
DOI: 10.1006/jsco.2001.0459