A note on the Stockhausen problem (Q1924233)

The paper solves problems related to the problem of determining the number of ways of performing a piano composition by Karlheinz Stockhausen. One problem out of this pile is the following: There are given \(n\) symbols. The paper determines the number and average length of those strings where (1) adjacent symbols are different, (2) the final symbol occurs \(r+1\) times, and (3) no other symbol occurs more then \(r\) times. Applying the answers for `Klavierstück XI' of Stockhausen (where \(n=19\) and \(r=2\)) there are more then \(10^{41}\) ways to perform it and an average performence consists of about 38 fragments.