A Computational Approach to Square Graham Partitions
Byungchan Kim, Eunmi Kim, Yoon Kyung Park · Experimental Mathematics · 2025
We propose an algorithm based on Monte Carlo Tree Search equipped with a supervised learned neural network to find an integer partition of n into squares satisfying n=λ1+λ2+⋯+λl,1=1λ1+1λ2+⋯+1λl with squares λ1≥λ2≥⋯≥λl≥1. By using induction and the search algorithm, we prove that such a partition exists if n≥1508.