✦ LIBER ✦
Sum-Free Subsets of Right Cancellative Semigroups
✍ Scribed by Tomasz Łuczak; Tomasz Schoen
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 112 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
✦ Synopsis
For a natural number k ≥ 2 let ρ = ρ(k) be the smallest natural number which does not divide k -1. We show that for any subset A of a right cancellative semigroup S which contains no solutions of the equation x 1 + • • • + x k = y there is an element s in S such that the sets A, A + s, . . . , A + (ρ -1)s are pairwise disjoint. In particular, if S is finite, such a set A has at most |S|/ρ elements. This estimate is sharp.