Journal
RAMANUJAN JOURNAL
Volume 50, Issue 1, Pages 211-235Publisher
SPRINGER
DOI: 10.1007/s11139-018-0030-y
Keywords
Exact covering system; Disjoint covering system; Natural exact covering system; Mobius function; Congruence; Constant gap sequence; Generating series; Asymptotics
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Funding
- NSERC Discovery Grants
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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 Sigma(k >= 1) mu(k)x(k), where mu(k) is the usual number-theoretic Mobius function. Using this result, we deduce an asymptotic expression for the number of such systems.
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