A NEW OPERATION ON PARTIALLY ORDERED SETS

Abstract. Recently it has been shown that all non-trivial closed permutation groups con-taining the automorphism group of the random poset are generated by two types of permu-tations: the first type are permutations turning the order upside down, and the second type are permutations induced by so-called rotations. In this paper we introduce rotations for finite posets, which can be seen as the poset counterpart of Seidel-switch for finite graphs. We analyze some of their combinatorial properties, and investigate in particular the question of when two finite posets are rotation-equivalent. We moreover give an explicit combinato-rial construction of a rotation of the random poset whose image is again isomorphic to the random poset. As an corollary of our results on rotations of finite posets, we obtain that the group of rotating permutations of the random poset is the automorphism group of a homogeneous structure in a finite language. 1. Operations from generic objects Switching of a graph was introduced by van Lint and Seidel in connection with a problem of finding equilateral n-tuples of points in elliptic geometry in 1966 [14]. The operation of switch or Seidel-switch on a graph with respect to a set X of vertices works as follows: interchang