Minimal complementary sets

Author:
Gerald Weinstein

Journal:
Trans. Amer. Math. Soc. **212** (1975), 131-137

MSC:
Primary 10J20

DOI:
https://doi.org/10.1090/S0002-9947-1975-0399023-0

MathSciNet review:
0399023

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Abstract: Let *G* be a group on which a measure *m* is defined. If we define . By we denote a subset of *G* consisting of *k* elements. Given we define and . Theorems 1, 2, and 3 deal with the problem of determining .

In the dual problem we are given *B*, , and required to find minimal *A* such that or, sometimes, . Theorems 5 and 6 deal with this problem.

**[1]**P. Erdös,*Some results on additive number theory*, Proc. Amer. Math. Soc.**5**(1954), 847-853. MR**16**, 336. MR**0064798 (16:336b)****[2]**G. G. Lorentz,*On a problem of additive number theory*, Proc. Amer. Math. Soc.**5**(1954), 838-841. MR**16**, 113. MR**0063389 (16:113f)****[3]**D. J. Newman,*Complements of finite sets of integers*, Michigan Math. J.**14**(1967), 481-486. MR**36**#1411. MR**0218324 (36:1411)****[4]**P. Erdös, Private communication.**[5]**G. Weinstein,*Some covering and packing results in number theory*, J. Number Theory (to appear). MR**0435022 (55:7984)**

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DOI:
https://doi.org/10.1090/S0002-9947-1975-0399023-0

Article copyright:
© Copyright 1975
American Mathematical Society