Computing maximal acyclic matchings

asked 2020-09-05 06:25:44 -0600

daltop gravatar image

updated 2020-09-05 06:28:11 -0600

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.

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FrédéricC gravatar imageFrédéricC ( 2020-09-05 06:41:25 -0600 )edit

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?

daltop gravatar imagedaltop ( 2020-09-05 07:30:23 -0600 )edit

NO. It will not enter sage until somebody takes care of all the necessary work required for this to happen. And nobody seems to care enough to take up the job.

FrédéricC gravatar imageFrédéricC ( 2020-09-05 12:02:45 -0600 )edit