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Distance-preserving subgraphs of hypercubes
Abstract We give a characterization of connected subgraphs G of hypercubes H such that the distance in G between any two vertices a, b ϵ G is the same as their distance in H. The hypercubes are
Classification of trivectors of an eight-dimensional real vector space
(1983). Classification of trivectors of an eight-dimensional real vector space. Linear and Multilinear Algebra: Vol. 13, No. 1, pp. 3-39.
Automorphisms of graphs and coverings
Abstract We apply the theory of covering spaces to show how one can construct infinitely many finite s -transitive or locally s -transitive graphs. N. Biggs has used for similar purpose a special
Closures of conjugacy classes in classical real linear Lie groups
By a classical group we mean one of the groups GLJ(R), GLn(C), GL,(H), U(p, q), OQ(C), O(p, q), SO*(2n), Sp21(C), Sp2n(R), or Sp(p, q). Let G be a classical group and L its Lie algebra. For each x E
Hermitian matrices over polynomial rings
Abstract Let R be a twisted polynomial ring F[X; S, D] where F is a division ring, S is an automorphism of F and D is an S-derivation of F. Thus Xα = αSX + αD holds for every α ϵ F. Let ∗ be an
Distillability and PPT entanglement of low-rank quantum states
It is known that he bipartite quantum states, with rank strictly smaller than the maximum of the ranks of its two reduced states, are distillable by local operations and classical communication. Our
Qubit-qudit states with positive partial transpose
We show that the length of a qubit-qutrit separable state is equal to the max(r,s), where r is the rank of the state and s is the rank of its partial transpose. We refer to the ordered pair (r,s) as
Normal forms of elements of classical real and complex Lie and Jordan algebras
Elements of the classical complex and real Lie and Jordan algebras with involutions are classified into conjugacy classes under the action of the corresponding classical Lie group. Normal forms of
Normal Forms and Tensor Ranks of Pure States of Four Qubits
We examine the SLOCC classification of the (non-normalized) pure states of four qubits obtained by F. Verstraete et al. The rigorous proofs of their basic results are provided and necessary