partially ordered set

The Green’s Relations and the Generalized Green’s Relations on Certain Transformation Semigroups

Authors: Kozhuhov I.

We investigate the Green’s relations L , R on the semigroups of isotone transformations of the partially ordered sets, and also the generalized Green’s relations L ∗, R∗ on the semigroup B(X) of binary relations on a set X. It is proved that L = L ∗, R = R∗ in the semigroup B(X) though this semigroup is non-regular for |X| > 3.

The Sperner Property for Polygonal Graphs Considered as Partially Ordered Sets

Authors: Salii V. N.

A finite poset is said to have the Sperner property if at least one of its maximum antichains is formed from elements of the same height. A polygonal graph is a directed acyclic graph derived from a circuit by some orientation of its edges. The reachability relation of a polygonal graph is a partial order. A criterion is presented for posets associated with polygonal graphs to have the Sperner property.