Minimal (max,+) Realization of Convex Sequences
Minimal (max,+) Realization of Convex Sequences
We show that the minimal dimension of a linear realization over the (max,+) semiring of a convex sequence is equal to the minimal size of a decomposition of the sequence as a supremum of discrete affine maps. The minimal-dimensional realization of any convex realizable sequence can thus be found in …