Ferdinands, Timothy; Pilkington, Annette A note on sums of roots. (English) Zbl 1431.17007 Rocky Mt. J. Math. 48, No. 3, 819-829 (2018). Summary: 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. Cited in 2 Documents MSC: 17B22 Root systems 20F55 Reflection and Coxeter groups (group-theoretic aspects) Keywords:root system; root sums Software:POSETS PDF BibTeX XML Cite \textit{T. Ferdinands} and \textit{A. Pilkington}, Rocky Mt. J. Math. 48, No. 3, 819--829 (2018; Zbl 1431.17007) Full Text: DOI Euclid References: [1] N. Bourbaki, Lie groups and Lie algebras, Springer-Verlag, Berlin, 2008. · Zbl 1145.17002 [2] B.A. Davey and H.A. Priestley, Introduction to lattices and order, Cambridge University Press, Cambridge, 2002. · Zbl 1002.06001 [3] M.J. Dyer and G.I. Lehrer, Parabolic subgroup orbits on finite root systems, J. Pure Appl. Alg., to appear. · Zbl 1398.20048 [4] C. Greene, POSETS package, http://ww3.haverford.edu/math/cgreene/posets.html. [5] R. Stanley, Enumerative combinatorics, Volume I, Wadsworth & Brooks/Cole, Monterey, CA, 1986. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.