O-aminophenol oxidase

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In mathematics, the Davenport constant of a group determines how large a subset can be without containing a set of elements which sum to zero. Its determination is an example of a zero-sum problem.

In general, a finite abelian group G is considered. The Davenport constant D(G) is the smallest integer d such that every sequence of elements of G of length d contains a non-empty subsequence with sum equal to the zero element of G.[1]

Examples

G=iCpei
then
D(G)=1+i(pei1).

Properties

  • For a finite abelian group
G=iCdi
with invariant factors d1|d2||dr, it is possible to find a sequence of i(di1) elements without a zero sum subsequence, so
D(G)M(G)=1r+idi.
  • It is known that D = M for p-groups and for r=1 or 2.
  • There are infinitely many examples with r at least 4 where D does not equal M; it is not known whether there are any with r = 3.[1]

References

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External links

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  1. 1.0 1.1 Bhowmik & Schlage-Puchta (2007)