In this article, we study the metacommutation problem in locally Eichler
orders. From this arises a permutation of the set of locally principal left
ideals of a given prime reduced norm...Previous results on the cycle structure
were determined for locally maximal orders. As we extend these results, we
present an alternative, combinatorial description of the metacommutation
permutation as an action on the Bruhat-Tits tree.(read more)