Non-simple polyominoes of Kőnig type and their canonical module

We study the K & odblac;nig type property for non-simple polyominoes. We prove that, for closed path polyominoes, the polyomino ideals are of K & odblac;nig type, extending the results of Herzog and Hibi for simple thin polyominoes. As an application of this result, we give a combinatorial interpretation for the canonical module of the coordinate ring of a sub-class of closed paths, namely circle closed path polyominoes. In this case, we compute also the Cohen-Macaulay type and we show that the coordinate ring is level.
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