4 problems

A pawn endgame on an $m\times n$ chessboard is a position in the generalized pawns game whose outcome is represented by a combinatorial-game-theoretic Nimber $*k$. The construction…

Nim-number spectrum conjecture. The spectrum of the nim number of avoidance games played in convex geometries is all nonnegative integers

For a game value $X$, let $f(X)$ be the minimum number of vertices in a digraph placement game having value $X$. For an integer $n\geq1$, let ${\ast n}$ denote the nimber of order…

Let $G$ be a finite group, and let $\text{\sf GEN}(G)$ denote its achievement game, with nim-number written as $*k$ for a nonnegative integer $k$. Even-order nimber conjecture. If…