I am recently doing some research related to the hook length formula. The hook formula counts the number of Young tableaux of certain type.

I find there are plenty of research already been done and I can observe a lot extension and generalization of hook length formula types. But is there a good survey on those research and open problems?

What I am interested are those extensions purely combinatorial, but it is still good if anybody can provide some survey on the representation theory side.

Please correct me if there are easy-to-find survey or the problem is too general for asking.

The Symmetric Group? $\endgroup$ – Nate Eldredge Mar 31 '15 at 21:34