Enumeration of Carlitz Multipermutations

Henrik Eriksson; Alexis Martin

Enumeration of Carlitz Multipermutations

Combinatorics 2017-02-20 v2

Authors: Henrik Eriksson , Alexis Martin

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.

Keywords

collatz conjecture permutations combinatorial bounds and extremal problems

Cite

@article{arxiv.1702.04177,
  title  = {Enumeration of Carlitz Multipermutations},
  author = {Henrik Eriksson and Alexis Martin},
  journal= {arXiv preprint arXiv:1702.04177},
  year   = {2017}
}

Comments

6 pages

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