Permutations Destroying Arithmetic Structure

[摘要] Given a linear form $C_1X_1 + \cdots + C_nX_n$, with coefficients in the integers, we characterize exactly the countably infinite abelian groups $G$ for which there exists a permutation $f$ that maps all solutions $(\alpha_1, \ldots , \alpha_n) \in G^n$

[学科分类] 离散数学和组合数学

[关键词] Pattern Avoidance;Abelian Groups;Arithmetic Progressions;Ramsey Theory