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On extremal $$h$$-bases $$A_4$$. (English) Zbl 0621.10039
For definition of the “postage stamp problem”, see E. S. Selmer [Math. Scand. 47, 29–71 (1980; Zbl 0436.10027)]. For $$k=4$$ and large $$h$$, the author considers the “global” stamp problem for a class of bases $$C$$. The author determines an optimal $$C$$ basis with $$h$$-range $$n(h,C)$$ such that for the extremal basis $$n(h,4)$$, $n(h,4)\geq n(h,C) = \sigma_ 4 (h/4)^4 + O(h^3)$ where $$\sigma_4>2.008$$. Since 1971 it seems to have been generally believed that $$\sigma_4=2$$ for the extremal basis.
Reviewer: Svein Mossige

##### MSC:
 11B13 Additive bases, including sumsets 11D04 Linear Diophantine equations
##### Keywords:
extremal basis; h-range; postage stamp problem
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