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{\bf Henrik Eriksson and Kimmo Eriksson}
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{\bf Affine Weyl Groups as Infinite Permutations}
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We present a unified theory for permutation models of all the
infinite families of finite and affine Weyl groups, including
interpretations of the length function and the weak order.
We also give new combinatorial proofs of Bott's formula (in the refined
version of Macdonald) for the Poincar\'e series of these affine Weyl groups.

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