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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The capacity of $ C\sb{5}$ and free sets in $ C\sb{m}\sp{2}$


Authors: D. G. Mead and W. Narkiewicz
Journal: Proc. Amer. Math. Soc. 84 (1982), 308-310
MSC: Primary 20D60; Secondary 10L02, 94A15
MathSciNet review: 637189
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Abstract: In a recent paper, S. K. Stein examined the problem of determining the cardinality, $ \tau (C_m^k)$, of the largest subset $ S$ of the direct product $ C_m^k$ of $ k$ copies of $ {C_m}$ such that distinct sums of elements of $ S$ yield distinct elements of $ C_m^k$. In this paper we show that $ {\tau ^* }({C_5}) = {\lim _{k \to \infty }}(\tau (C_5^k)/k) = 2$, answering a question raised by Stein. We also produce an infinite set of $ m$'s such that $ \tau (C_m^2) > 2[{\log _2}m]$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637189-4
PII: S 0002-9939(1982)0637189-4
Article copyright: © Copyright 1982 American Mathematical Society