Special solutions of discrete Painlevé equations through direct linearisation

We study the special solutions of discrete Painlevé equations which can be expressed through the discrete equivalent of quadratures. The discrete Painlevé equations examined are the ones which appear in the classification based on affine Weyl groups and which can be written as a system of two first-order mappings. The solutions obtained are the discrete equivalents of solutions which have been shown to exist for the continuous Painlevé equations.