至大小为 N=59 的多边形块的枚举
组合数学
2025-10-28 v1 离散数学
摘要
本文报告了数值计算结果，用于确定大小为 n 的多边形块（n 形块）的数量。我们验证了 n ≤ 50 的现有计数，并新计算出至 n ≤ 59 的多边形块总数，扩展了计数上限。该工作表明，除了优化多边形块计数问题的搜索算法外，多线程显著提高了计算效率。
引用
@article{arxiv.2510.22446,
title = {Enumeration of Polyominoes up to Size N=59},
author = {Toshihiro Shirakawa},
journal= {arXiv preprint arXiv:2510.22446},
year = {2025}
}
备注
Minor revision: Added the missing \section{Introduction} header. 11 pages, 3 figures. Includes two tables on computational resources and one main table of polyomino counts (physically split into 4 parts). Based on material presented at the 10th Gathering for Gardner (G4G10) in 2012