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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
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