Davenport constant formula for intervals containing zero

From papers

Let mm and MM be positive integers, and let D(m,M)\mathsf{D}(\llbracket -m,M \rrbracket) denote the maximal length of a minimal zero-sum sequence with terms in m,M\llbracket -m,M \rrbracket. Define

χ(m,M)=supx,ym,M with xy<0x+ygcd(x,y).\chi(\llbracket -m,M \rrbracket)=\sup_{x,y\in\llbracket -m,M \rrbracket\text{ with }xy<0}\frac{|x|+|y|}{\gcd(x,y)}.

Davenport constant conjecture for intervals.

D(m,M)=χ(m,M).\mathsf{D}(\llbracket -m,M \rrbracket)=\chi(\llbracket -m,M \rrbracket).

This conjecture gives a general formula for the Davenport constant of an interval of integers containing zero. The source paper states that it proves this conjecture, so the claim is solved.

Progress summary

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Sources & referencesView supporting material

Primary source

Benjamin Girard and Alain Plagne, “The Davenport constant of an interval: a proof that D=χ”, arXiv:2601.07950 (2026).

Additional references

4 papers in this index state this conjecture (2005–2026). The statement above is taken from the most recent of them; the others are arXiv:2407.01148, arXiv:1603.06030, arXiv:math/0509339.

Solutions 0

No solutions have been posted yet.