Enumeration of Carlitz Multipermutations

Abstract

A multipermutation with $k$ copies each of $1\dots n$ is Carlitz if neighbours are different. We enumerate these objects for $k=2,3,4$ and derive recurrences. In particular, we prove and improve a conjectured recurrence for $k=3$, stated in OEIS, the Online Encyclopedia of Integer Sequences.

6 pages