We generalize the results and conjectures of Tam\'{ a}s Lengyel, showing that the \textsc{ nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These are impartial, normal-play games with two piles of tokens, where players alternate either taking some tokens from a pile or transferring tokens from one pile to the other. In many cases, we calculate the exact period. We also develop several new notions of periodicitiy.
Categories: math.CO