Snevily's conjecture
From Groupprops
This article is about a conjecture in the following area in/related to group theory: additive combinatorics. View all conjectures and open problems
Contents
Statement
Let be an odd-order abelian group and be subsets of of equal cardinality. Then, there is a bijection such that the sums are distinct for all .
Relation with other conjectures
Progress towards the conjecture
For subsets of size two
Further information: Snevily's conjecture for subsets of size two
If are subsets of size two in an abelian group of odd order, Snevily's conjecture holds. This is easy to verify.
For cyclic groups
Further information: Snevily's conjecture for cyclic groups
Snevily's conjecture has been proved for groups of odd prime order by Alon, and for all odd-order cyclic groups by Dasgupta, Karolyi, Serra, and Szegedy.
References
Journal references
- Additive Latin transversals by Noga Alon, , Volume 117, Page 125 - 130(Year 2000): ^{PDF copy (Springerlink)}^{More info}
- Tranversals of additive Latin squares by Samit Dasgupta, Gyula Károlyi and Oriol Serra, , Volume 126, Page 17 - 28(Year 2001): ^{PDF copy (Springerlink)}^{More info}