AN ADDITIVE THEOREM AND RESTRICTED SUMSETS

作者：Sun Zhi Wei^*

来源：Mathematical Research Letters, 2008, 15(5-6): 1263-1276.

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)}(n)(i=1)of the elements of A, a numbering {b(i)}(n)(i=1) of the elements of B and a numbering {c(i)}(n)(i=1) of the elements of C, such that all the sums a(i) + b(i) + c(i) (1 <= i <= n) are (pairwise) distinct. Consequently, each subcube of the Latin cube formed by the Cayley addition table of Z/NZ contains a Latin transversal. This additive theorem is an essential result which can be further extended via restricted sumsets in a field.

• 出版日期2008-11
• 单位南京大学