Algorithmics of Posets Generated by Words Over Partially Commutative Alphabets (Extended)

It is natural to try to relate partially ordered sets (posets in short) and classes of equivalent words over partially commutative alphabets. Their common graphical representation are Hasse diagrams. We will investigate this relation in detail and propose an efficient on-line algorithm that decompresses a string to Hasse diagram. Further we propose a definition of the canonical representatives of classes of equivalent words. The advantage of this representation lies in the fact that we can enumerate the classes of equivalent words in a lexicographical order. We will give an algorithm which enumerates all distinct classes of words over partially commutative alphabets by their lexicographically minimal representatives.