Rényi entropy is subadditive on the majorization lattice for all alpha in [0, infinity] and supermodular for alpha in {0} union [1, infinity].
A finite sufficient set of conditions for catalytic majorization
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Geometry of R\'enyi Entropy on the Majorization Lattice
Rényi entropy is subadditive on the majorization lattice for all alpha in [0, infinity] and supermodular for alpha in {0} union [1, infinity].