Goulden, IP;
Granville, A;
Richmond, LB;
Shallit, J;
(2019)
Natural Exact Covering Systems and the Reversion of the Möbius Series.
The Ramanujan Journal
, 50
(1)
pp. 211-235.
10.1007/s11139-018-0030-y.
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Abstract
We prove that the number of natural exact covering systems of cardinality k is equal to the coefficient of xkin the reversion of the power series ∑k≥1μ(k) xk, where μ(k) is the usual number-theoretic Möbius function. Using this result, we deduce an asymptotic expression for the number of such systems.
| Type: | Article |
|---|---|
| Title: | Natural Exact Covering Systems and the Reversion of the Möbius Series |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11139-018-0030-y |
| Publisher version: | https://doi.org/10.1007/s11139-018-0030-y |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Exact covering system, Disjoint covering system, Natural exact covering system, Möbius function, Congruence, Constant gap sequence, Generating series , Asymptotics |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10060048 |
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