ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 05 Sep 2020 12:02:45 -0500Computing maximal acyclic matchingshttps://ask.sagemath.org/question/53313/computing-maximal-acyclic-matchings/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.Sat, 05 Sep 2020 06:25:44 -0500https://ask.sagemath.org/question/53313/computing-maximal-acyclic-matchings/Comment by FrédéricC for <p>Hi, Is there a function to compute the maximal acyclic (Morse) matching (defined below) of a given finite poset? </p>
<pre><code> 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.
</code></pre>
<p>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. </p>
<p>By maximal matching I mean one with the maximal number of elements. </p>
<p>Any help would be appreciated.</p>
https://ask.sagemath.org/question/53313/computing-maximal-acyclic-matchings/?comment=53321#post-id-53321NO. 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.Sat, 05 Sep 2020 12:02:45 -0500https://ask.sagemath.org/question/53313/computing-maximal-acyclic-matchings/?comment=53321#post-id-53321Comment by daltop for <p>Hi, Is there a function to compute the maximal acyclic (Morse) matching (defined below) of a given finite poset? </p>
<pre><code> 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.
</code></pre>
<p>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. </p>
<p>By maximal matching I mean one with the maximal number of elements. </p>
<p>Any help would be appreciated.</p>
https://ask.sagemath.org/question/53313/computing-maximal-acyclic-matchings/?comment=53317#post-id-53317I 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?Sat, 05 Sep 2020 07:30:23 -0500https://ask.sagemath.org/question/53313/computing-maximal-acyclic-matchings/?comment=53317#post-id-53317Comment by FrédéricC for <p>Hi, Is there a function to compute the maximal acyclic (Morse) matching (defined below) of a given finite poset? </p>
<pre><code> 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.
</code></pre>
<p>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. </p>
<p>By maximal matching I mean one with the maximal number of elements. </p>
<p>Any help would be appreciated.</p>
https://ask.sagemath.org/question/53313/computing-maximal-acyclic-matchings/?comment=53314#post-id-53314See https://trac.sagemath.org/ticket/26222 (not yet in sage)Sat, 05 Sep 2020 06:41:25 -0500https://ask.sagemath.org/question/53313/computing-maximal-acyclic-matchings/?comment=53314#post-id-53314