Is there a Mathematica implementation/package that displays all topological sorts (i.e. linear extensions) of a partial order using labelled Hasse diagrams (nodes labeled with the appropriate topological sort values)?
For instance, consider the partial order determined by the pairs (a,c), (b,c) (two independent elements a and b, with a maximum c above it in the Hasse diagram). Is there a package to display the two topological sorts (linear extensions) using the numbers 1, 2, 3 via labeled Hasse Diagrams? In the first labeled Hasse Diagram, the node a is labeled with 1, b with 2 and c with 3. In the second labeled Hasse diagram, the node a is labeled with 2, b with 1 and c with 3. The Hasse diagram is displayed as a "hat"-shaped (^) graph, with labels.
I would need code that is adaptable to move labels around via various operations. So a proprietary package from Mathematica for which code is not accessible would not help.