A complexity theorem for the Novelli-Pak-Stoyanovskii algorithm

We describe two aspects of the behaviour of entries of Young tableaux during the application of the Novelli-Pak-Stoyanovskii algorithm. We derive two theorems which both contain a generalized version of a conjecture by Krattenthaler and M"uller concerning the complexity of the Novelli-Pak-Stoyanovskii algorithm as corollary.