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Nov 20 at 1:07 comment added Richard Stanley There are a vast number of papers on special cases, one example being Goupil's paper at sciencedirect.com/science/article/pii/0012365X9090054L. I wouldn't be surprised if the general problem is #P-complete. Maybe this is already known. See also inria.hal.science/inria-00098749/document.
Nov 19 at 5:08 comment added user545662 I don't know if there are some estimates or specific properties on these numbers just combinatorically. Or it is just too difficult to calculate directly?
Nov 18 at 11:42 comment added Richard Stanley Essentially a repeat of mathoverflow.net/questions/62088.
Nov 18 at 10:28 history edited YCor CC BY-SA 4.0
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Nov 18 at 7:03 comment added Fedor Petrov There are many results, so what do you need?
S Nov 18 at 2:41 review First questions
Nov 18 at 5:39
S Nov 18 at 2:41 history asked user545662 CC BY-SA 4.0