• Corpus ID: 214612366

Cantor-solus and Cantor-multus Distributions

@article{Finch2020CantorsolusAC,
  title={Cantor-solus and Cantor-multus Distributions},
  author={Steven R. Finch},
  journal={ArXiv},
  year={2020},
  volume={abs/2003.09458}
}
  • S. Finch
  • Published 20 March 2020
  • Mathematics
  • ArXiv
The Cantor distribution is obtained from bitstrings; the Cantor-solus distribution (a new name) admits only strings without adjacent 1 bits. We review moments and order statistics associated with these. The Cantor-multus distribution is introduced -- which instead admits only strings without isolated 1 bits -- and more complicated formulas emerge. 

Variance of Longest Run Duration in a Random Bitstring

While negative correlations approach zero as n approaches zero as $n \rightarrow \infty$ in the former (for clumped 1s), the limit is evidently nonzero in the latter (for separated 1s).

C O ] 1 3 O ct 2 02 0 Covariance within Random Integer Compositions

Fix a positive integer N . Select an additive composition ξ of N uniformly out of 2N−1 possibilities. The interplay between the number of parts in ξ and the maximum part in ξ is our focus. It is not

Covariance within Random Integer Compositions

It is given inconclusive evidence that $\lim_{N \to \infty} \rho(N)$ is strictly less than zero; a proof of this result would imply asymptotic dependence, and the presumption in such an unforeseen outcome is retracted.

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