Vanishing of Doubly Symmetrized Tensors

Andrew Berget, J. A. Dias da Silva, Amélia Fonseca


Symmetrizations of tensors by irreducible characters of the symmetric group serve as natural analogues of symmetric and skew-symmetric tensors. The question of when a symmetrized decomposable tensor is non-zero is intimately related to the rank partition of a matroid extracted from the tensor. In this paper we characterize the non-vanishing of the symmetrization of certain partially symmetrized decomposable tensors. Our answers are phrased in terms of rank partitions of matroids.


symmetrizations of tensors, matroid, rank partition

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