Positive posets with linear Hasse diagrams

Abstract

This paper studies positive (i.e., with positive Tits quadratic form) posets whose Hasse diadrams are linear. A criterion for the existence of such a nonserial poset of an arbitrary fixed order and height (width) is provided. We do not use the previously obtained by us complete list of nonserial positive posets, which contains 108 elements up to isomorphism and duality.