CPL - Chalmers Publication Library

# The postage stamp problem and essential subsets in integer bases

Peter Hegarty (Institutionen för matematiska vetenskaper, matematik)
David and Gregory Chudnovsky (eds.), Additive Number Theory : Festschrift in Honor of the Sixtieth Birthday of Melvyn B. Nathanson. Springer-Verlag, New York. p. 153-171. (2010)
[Kapitel]

Plagne recently determined the asymptotic behavior of the function E(h), which counts the maximum possible number of essential elements in an additive basis for N of order h. Here we extend his investigations by studying asymptotic behavior of the function E(h,k), which counts the maximum possible number of essential subsets of size k, in a basis of order h. For a fixed k and with h going to infinity, we show that E(h,k) = \Theta_{k} ([h^{k}/\log h]^{1/(k+1)}). The determination of a more precise asymptotic formula is shown to depend on the solution of the well-known "postage stamp problem" in finite cyclic groups. On the other hand, with h fixed and k going to infinity, we show that E(h,k) \sim (h-1) {\log k \over \log \log k}.

CPL Pubid: 75262

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# Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)