Plethysm coefficients are important structural constants in the representation the-
ory of the symmetric groups and general linear groups. Remarkably, some sequences
of plethysm coefficients stabilize (they are ultimately constants). In this paper we
give a new proof of such a stability property, proved by Brion with geometric representation theory techniques. Our new proof is purely combinatorial: we decompose
plethysm coefficients as a alternating sum of terms counting integer points in poly-
topes, and exhibit bijections between these sets of integer points.Ministerio de Ciencia e Innovación MTM2010–19336Junta de Andalucía FQM–333Junta de Andalucía P12–FQM–269