Mixing properties of colourings of the ℤ d lattice
Mixing properties of colourings of the ℤ d lattice
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∄d 晶格着色的混合特性
DOI：
10.1017/s0963548320000395
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Spinka, Yinon
中科院分区：
文献类型：
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作者：
Alon, Noga;Briceño, Raimundo;Chandgotia, Nishant;Magazinov, Alexander;Spinka, Yinon
我们研究并分类了ℤ-d格的适当Q-染色，确定了三个不同组合行为成立的区域。(1)当存在冻结染色时，即ℤd的真q-染色不能在任何有限子集上修改。(2)我们证明了一个强列表着色性质，它意味着，当边长的盒的边界的任何适当的q-着色都可以推广到整个盒的真正的q-着色时。(3)在任何情况下，后者在任何情况下均成立。因此，我们根据混合性质对ℤ-d格的真q-染色空间进行了分类。
We study and classify proper q-colourings of the ℤd lattice, identifying three regimes where different combinatorial behaviour holds. (1) When , there exist frozen colourings, that is, proper q-colourings of ℤd which cannot be modified on any finite subset. (2) We prove a strong list-colouring property which implies that, when , any proper q-colouring of the boundary of a box of side length can be extended to a proper q-colouring of the entire box. (3) When , the latter holds for any . Consequently, we classify the space of proper q-colourings of the ℤd lattice by their mixing properties.