Stanley sequences with odd character (1707.02037v2)

Abstract: Given a set of integers containing no 3-term arithmetic progressions, one constructs a Stanley sequence by choosing integers greedily without forming such a progression. Independent Stanley sequences are a "well-structured" class of Stanley sequences with two main parameters: the character $\lambda(A)$ and the repeat factor $\rho(A)$. Rolnick conjectured that for every $\lambda \in \mathbb{N}_0\backslash{1, 3, 5, 9, 11, 15}$, there exists an independent Stanley sequence $S(A)$ such that $\lambda(A) =\lambda$. This paper demonstrates that $\lambda(A) \not\in {1, 3, 5, 9, 11, 15}$ for any independent Stanley sequence $S(A)$.