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arXiv · 1407.4514

Symmetric 1-Dependent Colorings of the Integers

Alexander E. Holroyd·Thomas M. Liggett
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Abstract

In a recent paper by the same authors, we constructed a stationary 1-dependent 4-coloring of the integers that is invariant under permutations of the colors. This was the first stationary k-dependent q-coloring for any k and q. When the analogous construction is carried out for q>4 colors, the resulting process is not k-dependent for any k. We construct here a process that is symmetric in the colors and 1-dependent for every q>=4. The construction uses a recursion involving Chebyshev polynomials evaluated at $\sqrt{q}/2$.

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Alexander E. Holroyd, Thomas M. Liggett. 2014-07-16. Symmetric 1-Dependent Colorings of the Integers. https://arxiv.org/abs/1407.4514

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