5 problems

Let $G$ be a commutative group, and let an Ulam set in $G$ be generated from two initial generators using unique sums of two earlier distinct elements. Two-generator infinitude con…

Let $\mathcal{U}$ be an Ulam set with two generators, and suppose its associated lattice is nonzero. Each $u\in\mathcal{U}$ has a canonical contribution vector…

Let $a>2$ be even and let $b$ be sufficiently large. Consider an Ulam set with generators $v_1$ and $v_2$ whose associated lattice is generated by $(-a,b)$. Regularity conjecture.…

An Ulam sequence in $\mathbb{Z}$ is generated by an initial set under the rule that a new element is included when it has a unique representation as the sum of two distinct earlier…

Let $mathcal{W}{2,n}$ denote the set of binary words of length $n$, and let $Vn=mathcal{U}({0,1})capmathcal{W}{2,n}$. The density of the binary Ulam set is measured by…