6 problems

Period conjecture. The Nim value function is periodic with a period equal to one of $a+b$, $b+c$, or $c+a$.

White-region non-periodicity conjecture. The Nim value function for $W_n$ is not purely periodic with any period, and each $W_n$ is split into infinitely many parts.

Ward's period conjecture. The Nim value function has a period equal to one of $a+b$, $b+c$, or $c+a$.

Consider subtraction Nim with subtraction set $\{s_1,s_2,s_3\}$ and one pass. Let $\mathcal{G}(x,0)$ denote the Grundy number without a pass and $\mathcal{G}(x,1)$ the Grundy numbe…

Consider the three-element subtraction Nim setup above, including the eventual period $p$ and the associated distance function $dist(w)$. The reverse-mex condition. If…

The reverse-mex characterization. The subtraction Nim has the reverse-$mex$ property if and only if, for every $\mathcal{P}$-position $w$ with $dist(w)=2m$ for some…