6 problems

Let $\mathcal{C}$ be a cut set satisfying … and suppose that $\mathcal{C}\neq\{1,2\}$. This is Family C. Family C arithmetic-periodicity conjecture. The nim-sequence for every game…

Family B partial conjecture. If $3x<y$, then

Family A arithmetic-periodicity conjecture. The nim-sequence for every game of textsc{cut} in this family is precisely $(0,1)^c (+2)$. This concerns one of the families whose nim-s…

Period characterization conjecture. In Case I,

Let $(a_i)_{i=0}^n$ with $n\geq2$ be a finite representing sequence with representation word $w$, and let $m$ be an integer with $n\geq2$. Define $(b_i)$ by … and let $v$ be the re…

Period formula conjecture. If there exists a multiple $m$ of $2a$ satisfying