Publication Date:
2012-05-15
Description:
Let ( G , +) be a finite abelian group. Then, S ( G ) and ( G ) denote the smallest integer such that each sequence over G of length at least has a subsequence whose terms sum to 0 and whose length is equal to and at most, respectively, the exponent of the group. For groups of rank 2, we study the inverse problems associated to these constants, that is, we investigate the structure of sequences of length S ( G )–1 and ( G )–1 that do not have such a subsequence. On the one hand, we show that the structure of these sequences is in general richer than expected. On the other hand, assuming a well-supported conjecture on this problem for groups of the form C m C m , we give a complete characterization of all these sequences for general finite abelian groups of rank 2. In combination with partial results towards this conjecture, we get unconditional characterizations in special cases.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
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