Two Dimensional Subtraction -- Transfer Games
Combinatorics
2026-05-25 v2
Abstract
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.
Cite
@article{arxiv.2602.14325,
title = {Two Dimensional Subtraction -- Transfer Games},
author = {Alon Danai and Paul Ellis and Thotsaporn Aek Thanatipanonda},
journal= {arXiv preprint arXiv:2602.14325},
year = {2026}
}
Comments
16 pages, 16 figures