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.
@article{10_37236_3266,
author = {Andrew Berget and J. A. Dias da Silva and Am\'elia Fonseca},
title = {Vanishing of doubly symmetrized tensors},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {2},
doi = {10.37236/3266},
zbl = {1295.15015},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3266/}
}
TY - JOUR
AU - Andrew Berget
AU - J. A. Dias da Silva
AU - Amélia Fonseca
TI - Vanishing of doubly symmetrized tensors
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/3266/
DO - 10.37236/3266
ID - 10_37236_3266
ER -
%0 Journal Article
%A Andrew Berget
%A J. A. Dias da Silva
%A Amélia Fonseca
%T Vanishing of doubly symmetrized tensors
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/3266/
%R 10.37236/3266
%F 10_37236_3266
Andrew Berget; J. A. Dias da Silva; Amélia Fonseca. Vanishing of doubly symmetrized tensors. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/3266
