Hook length formulas relating sums over different partition sizes.

R.P. Stanley's and G-N. Han's work in 2008-2009 on Hook length formulas do not seem to connect sums over partitions of different sizes. I mean relations between sums over partitions of n-1, of n and of n+1. I got one, but do not know if I should be surprised or not. It takes a better mathematician to distinguish between the boring and the interesting tidbits.

Since I'm a hopeless dud at LaTeX, forgive me replacing it with a link to a PDF file with the accompanying short Mathematica 4.0 notebook:

http://users.telenet.be/Wouter.Meeussen/MildlySurprisingHooks.pdf http://users.telenet.be/Wouter.Meeussen/MildlySurprisingHooks.nb

flag	asked Apr 30 2012 at 12:11 Wouter Meeussen 1

Your pdf file does not display correctly on my computer and is unreadable. – Richard Stanley Apr 30 2012 at 16:10

Wouter Meeussen: I've deleted your reply, which reads, "Indeed, sorry. Should be cured now." If you register an account, you won't have to worry about unintentionally creating new ones. – S. Carnahan♦ Jul 11 at 4:53