平面網格雙色頂點著色的正熵問題

Abstract

本篇論文討論給定一個頂點著色地磚(tiles)集合，熵(spatial entropy)是正值或零並非由集合裡的最小週期生成子集(minimal cycle generators)決定；考慮一個最小週期生成子集的聯集並且其熵為零。在此聯集中加入tiles而不產生新的最小週期生成子集後，熵可能會由零轉變為正值。

In this paper we consider a given basic set of corner-coloring tiles, the spatial entropy is positive or zero cannot be determined by studying a union of minimal cycle generators. Consider a union of minimal cycle generators with zero entropy. If we add tiles into the union without producing new minimal cycle generators, then the spatial entropy possibly turns from zero to positive.