A necessary and sufficient condition is given for reducibility of a symmetric polynomial whose number of variables is large in comparison to degree.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-2,
author = {A. Schinzel},
title = {Reducibility of Symmetric Polynomials},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {251-258},
zbl = {1106.12002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-2}
}
A. Schinzel. Reducibility of Symmetric Polynomials. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 251-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-2/