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Creators/Authors contains: "Briceño, Raimundo"

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  1. ; ; ; ; (, Combinatorics, Probability and Computing)
    Abstract We study and classify proper q -colourings of the ℤ d lattice, identifying three regimes where different combinatorial behaviour holds. (1) When $$q\le d+1$$ , there exist frozen colourings, that is, proper q -colourings of ℤ d which cannot be modified on any finite subset. (2) We prove a strong list-colouring property which implies that, when $$q\ge d+2$$ , any proper q -colouring of the boundary of a box of side length $$n \ge d+2$$ can be extended to a proper q -colouring of the entire box. (3) When $$q\geq 2d+1$$ , the latter holds for any $$n \ge 1$$ . Consequently, we classify the space of proper q -colourings of the ℤ d lattice by their mixing properties. 
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