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New York Journal of Mathematics 8 (2002), 63-83.

Asymptotic density in combined number systems

Karen Yeats

Published: April 12, 2002
Keywords: additive number system, multiplicative number system, asymptotic density, partition set, ratio test, regular variation
Subject: Primary 11N45, 11P99, Secondary 05A16, 11N80


Necessary and sufficient conditions are found for a combination of additive number systems and a combination of multiplicative number systems to preserve the property that all partition sets have asymptotic density. These results cover and extend several special cases mentioned in the literature and give partial solutions to two problems in [6].

Thanks to Stan Burris, a patient and meticulous supervisor, to the referee for his interest and detailed comments, and to NSERC for their Undergraduate Student Research Award which supported this research.

Author information:
Department of Pure Mathematics ,University of Waterloo ,Waterloo Ontario,N2L 3G1 ,Canada