5 problems

Fix integers $c,h\geq0$, and for each $n\geq2$ let … Suppose that $\Delta(S_2)=\{1,c_0,c_1,\ldots,c_k\}$. The generalization conjecture. Then … Moreover, for $c\geq4$, $x\geq2$, an…

The conjecture. $\Delta(S)=\{1,2,3\}$. For $x\geq3$, if

Let $m\geq 1$ and $k\geq 0$ be integers, and let … For each $i\in[1,m]$, let … where the first $2$ is in position $i+1$ and the $1$ is in position $i+2$, counting positions from…

BCLMS conjectures. If $|\Delta(S)|>1$, then $2d\in\Delta(S)$. If $|\Delta(S)|>2$, then $3d\in\Delta(S)$. These conjectures refine the realization problem for delta sets by predicti…

Let $S$ be a numerical semigroup of embedding dimension three, and let $t$ be an integer with $t\geq 3$. BCLMS conjecture. The set $\{1,t\}$ cannot occur as the delta set of $S$. T…