Arc permutations

Arc permutations and unimodal permutations were introduced in the study of triangulations and characters. This paper studies combinatorial properties and structures on these permuta-tions. First, both sets are characterized by pattern avoidance. It is also shown that arc permu-tations carry a natural affine Weyl group action, and that the number of geodesics between a distinguished pair of antipodes in the associated Schreier graph, as well as the number of maxi-mal chains in the weak order on unimodal permutations, are both equal to twice the number of standard Young tableaux of shifted staircase shape. Finally, a bijection from non-unimodal arc permutations to Young tableaux of certain shapes, which preserves the descent set, is describe