## AbstractIn this paper we address the task of discovering the local ordering relationships that better summarize a set of input sequences. We contribute by characterizing the notion of closed partial orders and showing that their organization in a lattice framework gives a final global overview of the ordered dataset. As a main result, we prove that the maximal paths of these closed partial orders are indeed a simple set of so-called stable sequences; thus, the set of all closed partial orders can be obtained via an easy transformation on groups of these stable patterns. In the practice, this transformation implies that algorithms for mining stable sequences can efficiently convert their patterns into closed partial orders, avoiding the complexity of the mining operation of these structures directly from the data. We illustrate our approach by applying it to unix user command data.
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