# Enumeration of Carlitz Multipermutations

## TL;DR

This paper enumerates Carlitz multipermutations with specific repetitions, deriving recurrences and confirming a conjecture for the case of three copies, thereby advancing combinatorial enumeration techniques.

## Contribution

It provides explicit enumeration formulas and recurrences for Carlitz multipermutations with k=2,3,4, including a proof and improvement of a conjectured recurrence for k=3.

## Key findings

- Derived recurrences for k=2,3,4 cases
- Proved and improved a conjectured recurrence for k=3
- Enumerated Carlitz multipermutations for small k values

## Abstract

A multipermutation with $k$ copies each of $1\ldots n$ 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.