Two Dimensional Subtraction -- Transfer Games

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Alon Danai, Paul Ellis, Thotsaporn Thanatipanonda
DOI: 10.48550/arxiv.2602.14325
Cited by: 0

Abstract

We generalize the results and conjectures of Tamás 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.

Fields of Study & Subjects

Advanced Combinatorial Mathematics Game Theory and Applications Limits and Structures in Graph Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
15 February 2026
Language
EN
Document type
Preprint