• Corpus ID: 220250400

Difference Necklaces

@article{White2020DifferenceN,
  title={Difference Necklaces},
  author={E. P. White and Richard K. Guy and Renate Scheidler},
  journal={arXiv: Combinatorics},
  year={2020}
}
An $(a,b)$-difference necklace of length $n$ is a circular arrangement of the integers $0, 1, 2, \ldots , n-1$ such that any two neighbours have absolute difference $a$ or $b$. We prove that, subject to certain conditions on $a$ and $b$, such arrangements exist, and provide recurrence relations for the number of $(a,b)$-difference necklaces for $( a, b ) = ( 1, 2 )$, $( 1, 3 )$, $( 2, 3 )$ and $( 1, 4 )$. Using techniques similar to those employed for enumerating Hamiltonian cycles in certain… 

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