Enumeration of Polyominoes up to Size N=59

2025/10/25 by Shirakawa, Toshihiro
#05B50 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #F.2.2 #FOS: Computer and information sciences #FOS: Mathematics #G.2.1

paper · doi:10.48550/arxiv.2510.22446

Abstract

This paper reports the results of numerical computations for determining the number of polyominoes of size n (n-ominoes). We verify the existing counts for n <= 50 and newly compute the total number of polyominoes up to n <= 59, extending the counting limit. This work shows that, in addition to optimizing the search algorithm for the polyomino counting problem, multi-threading dramatically improves computational efficiency.

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