\magnification=1440 \font\bigtenrm=cmr10 scaled\magstep4 Abstract for Anders Bj\"orner and Francesco Brenti, Affine Permutations of Type $A$ We study combinatorial properties, such as inversion table, weak order and Bruhat order, for certain infinite permutations that realize the affine Coxeter group $\tilde{A}_{n}$. \bye .