# Timeline for Counting the number of matchings in a complete bipartite graph

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Nov 21 '20 at 16:44 history edited
Added no-good inequalties, a tag, and an explanation for the mismatch in the numbers
Nov 21 '20 at 15:35 comment @prubin obviously I'm using the wrong terminology. The IP is the corret one, so maybe what I am counting is the number of semi-assignments. The idea is to count how many ways $n$ jobs can be assigned to $n$ agents if each agent in principle can handle all items, and all items need to be handled.
Nov 20 '20 at 23:34 answer timeline score: 8
Nov 20 '20 at 22:15 history became hot network question
Nov 20 '20 at 21:54 comment To get a valid matching, shouldn't you constraint $\sum_j x_{ij} \le 1$ for all $i$ (no repetitions of left endpoint)? Also, by making your constraint equality rather than inequality, aren't you skipping (imperfect) matchings that miss some right endpoints?
Nov 20 '20 at 21:05 comment Can you include the no-good cut that you use?
Nov 20 '20 at 14:45 answer timeline score: 3
Nov 20 '20 at 14:41 history edited
[Edit removed during grace period]; edited body
Nov 20 '20 at 14:15 history asked