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I am not familiar with the Sage, but I understand from the information on that link, that the function I ask for will be ready in Sage 9.3 in just 3 weeks?

Hi, Is there a function to compute the maximal acyclic (Morse) matching (defined below) of a given finite poset?

 A matching  M in a poset X is a subset M of X x X such that:
   1) if (x, y) is in M, then x is an immediate predecessor of y (x<y and there is no element z such that x<z<y)
   2) each element x of X belongs to at most one element in M.

In order to represent the matching on the associated Hasse Diagram of the poset, we just reverse the arrows which are not in the matching. The matching is acyclic (Morse) if the matching represented on its Hasse Diagram is acyclic.

By maximal matching I mean one with the maximal number of elements.

Any help would be appreciated.

Hi,

I would like to know how to find a maximal matching (defined below) of a given finite poset.

 A matching  M in a poset X is a subset M of X x X such that:
   1) if (x, y) is in M, then x is an immediate predecessor of y (x<y and there is no element z such that x<z<y)
   2) each element x of X belongs to at most one element in M.

A matching of a poset is the same as a matching of its Hasse Diagram. I thought about using the matching() function for graphs, however, it seems that the Hasse diagram of a poset is a Digraph for Sage and so the matching function does not work.

By maximal matching I mean one with the maximal number of elements.

Any help would be appreciated.