Is there any connection at all between the Gamma Function and the theory/enumeration of ordered sets and lattices?
I mean, the factorial function, amongst other things, counts the number of linear orders or chains on an n-element set (by the notation n!).
Linear orders are critical in the study of ordered sets and lattices, via the order dimension and various other constructs.
It seems kinda hopeless: linear orders have a nice formula but (partially) ordered sets and lattices do not, whether labelled or unlabelled.
And yet it seems (just to me) odd somehow to have this obvious enumerative connection with the ways to linearly order a set (an object critical in order theory) and the Gamma function, and then just... that's it.