Sign Types Associated to Posets

We start with a combinatorial definition of I-sign types which are a generalization of the sign types indexed by the root system of type Al (I⊂N finite). Then we study the set DIp of I-sign types associated to the partial orders on I. We establish a 1–1 correspondence between D[n]p and a certain set of polyhedral cones in a euclidean space by which we get a geometric distinction of the sign types in D[n]p from the other [n]-sign types. We give a graph-theoretical criterion for an Sn-orbit O of D[n]p to contain a dast and show that O contains at most one dast. Finally, we show the admirability of a poset associated to a dast.