Mathematics – Number Theory
Scientific paper
2008-07-02
Mathematics
Number Theory
15 pages, no figures
Scientific paper
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}.
No associations
LandOfFree
The Postage Stamp Problem and Essential Subsets in Integer Bases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Postage Stamp Problem and Essential Subsets in Integer Bases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Postage Stamp Problem and Essential Subsets in Integer Bases will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-115077