In this paper, we look at properties of roots which can be written as sums of roots in crystallographic root systems. We derive properties of the poset associated to such a sum consisting of the subsums which are themselves roots.
"A note on sums of roots." Rocky Mountain J. Math. 48 (3) 819 - 829, 2018. https://doi.org/10.1216/RMJ-2018-48-3-819