There is a topological conjugation between piecewise increasing linear and piece- wise expanding interval maps. Properties of such maps can be studied through the piecewise linear case. This case has connections with number theory, e.g. the Gauss- Gegenbauer generalization of Fermat’s little theorem, and with combinatorics on words, through bijections between the set of periodic orbits (periodic points) and the set of necklaces (words).