Galois covering technique and tame non-simply connected posets of polynomial growth

A combinatorial criterion for polynomial growth of partially ordered sets which are not simply connected is given. It is obtained by use of Galois covering techniques applied to poset representations. For this purpose a relative version of the basic Galois covering theory of k-categories is developed in the paper. The remaining part of the proof of the main result is based on standard methods like “peak reductions” and Splitting Lemma used in the theory of multipeak posets.