An additive theorem and restricted sumsets

Details An additive theorem and restricted sumsets An additive theorem and restricted sumsets

2006-10-31

arxiv.org/abs/math/0610981v7

Math. Res. Lett. 15(2008), no.6, 1263-1276

Mathematics

Combinatorics

Scientific paper

Let G be any additive abelian group with cyclic torsion subgroup, and let A, B and C be finite subsets of G with cardinality n>0. We show that there is a numbering {a_i}_{i=1}^n of the elements of A, a numbering {b_i}_{i=1}^n of the elements of B and a numbering {c_i}_{i=1}^n of the elements of C, such that all the sums a_i+b_i+c_i (i=1,...,n) are distinct. Consequently, each subcube of the Latin cube formed by the Cayley addition table of Z/NZ contains a Latin transversal. This additive theorem can be further extended via restricted sumsets in a field.

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