In [LJ06] Lorenz and Juh´as raised the question of whether there exists a suitable formalism for the representation of inﬁnite families of partial orders generated by Petri nets. Restricting ourselves to bounded p/t-nets, we propose Hasse diagram generators as an answer. We show that Hasse diagram generators are expressive enough to represent the partial order language of any bounded p/t net. We prove as well that it is decidable both whether the (possible inﬁnite) family of partial orders represented by a given Hasse diagram generator is included on the partial order language of a given p/t-net and whether their intersection is empty. Based on this decidability result, we prove that the partial order languages of two given Petri nets can be eﬀectively compared with respect to inclusion. Finally we address the synthesis of k-safe p/t-nets from Hasse diagram generators. Key words: Causality/partial order theory of concurrency.