Affine permutations of type \(A\)
Let \(\widetilde S_n\) denote the group (under composition) of all bijections \(\pi: \mathbb{Z}\to \mathbb{Z}\) such that \(\pi(x)+ n= \pi(x+ n)\) for all \(x\in \mathbb{Z}\), and \(\pi(1)+ \pi(2)+\cdots+ \pi(n)= (\begin{smallmatrix} n+ 1\\ 2\end{smallmatrix})\). This gives a realization of the affine Coxeter group \(\widetilde A_{n- 1}\). The authors study combinatorial properties of such affine permutations, such as the inversion table, weak order and Bruhat order.
scientific article; zbMATH DE number 907657