  We investigate the descriptional complexity of operations on semilinear sets.
Roughly speaking, a semilinear set is the finite union of linear sets, which
are built by constant and period vectors. The interesting parameters of a
semilinear set are: (i) the maximal value that appears in the vectors of
periods and constants and (ii) the number of such sets of periods and constants
necessary to describe the semilinear set under consideration. More precisely,
we prove upper bounds on the union, intersection, complementation, and inverse
homomorphism. In particular, our result on the complementation upper bound
answers an open problem from [G. J. LAVADO, G. PIGHIZZINI, S. SEKI: Operational
State Complexity of Parikh Equivalence, 2014].
