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- W4360945750 abstract "Let G ⩽ Sym ( X ) $G leqslant mathrm{Sym}(X)$ be a group of permutations of a countable set X $X$ . Call a colouring of X $X$ asymmetric if no g ∈ G ∖ { id } $g in G setminus lbrace mathrm{id}rbrace$ preserves all colours. The motion of G $G$ is the minimal number of elements moved by an element g ∈ G ∖ { id } $g in G setminus lbrace mathrm{id}rbrace$ . We show that if G $G$ is locally compact with respect to the permutation topology and the motion of G $G$ is infinite, then there is an asymmetric 2-colouring of X $X$ . This builds on a recent result by Babai, generalises this result, and confirms a conjecture by Imrich, Smith, Tucker, and Watkins from 2015." @default.
- W4360945750 created "2023-03-26" @default.
- W4360945750 creator A5028836452 @default.
- W4360945750 date "2023-03-25" @default.
- W4360945750 modified "2023-10-10" @default.
- W4360945750 title "Asymmetric colouring of locally compact permutation groups" @default.
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- W4360945750 doi "https://doi.org/10.1112/blms.12824" @default.
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