A Symmetric Functions Approach to Stockhausen's Problem

We consider problems in sequence enumeration suggested by Stockhausen’s problem, and derive a generating series for the number of sequences of length k on n available symbols such that adjacent symbols are distinct, the terminal symbol occurs exactly r times, and all other symbols occur at most r − 1 times. The analysis makes extensive use of techniques from the theory of symmetric functions. Each algebraic step is examined to obtain information for formulating a direct combinatorial construction for such sequences.