Maximum antichains in posets of quiver representations

Gellert F, Lampe P. Maximum antichains in posets of quiver representations. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 2018;59(1):1-20.We study maximum antichains in two posets related to quiver representations. Firstly, we consider the set of isomorphism classes of indecomposable representations ordered by inclusion. For various orientations of the Dynkin diagram of type A we construct a maximum antichain in the poset. Secondly, we consider the set of subrepresentations of a given quiver representation, again ordered by inclusion. It is a finite set if we restrict to linear representations over finite fields or to representations with values in the category of pointed sets. For particular situations we prove that this poset is Sperner