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Natural exact covering systems and the reversion of the M��bius series
- Publication Year :
- 2017
- Publisher :
- arXiv, 2017.
-
Abstract
- We prove that the number of natural exact covering systems of cardinality $k$ is equal to the coefficient of $x^k$ in the reversion of the power series $\sum_{k \ge 1} ��(k) x^k$, where $��(k)$ is the usual number-theoretic M��bius function. Using this result, we deduce an asymptotic expression for the number of such systems.
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi...........cd67432ba7c7881a7a60e47f660c05a9
- Full Text :
- https://doi.org/10.48550/arxiv.1711.04109