Forbidden configurations for distributive, modular and semidistributive posets

摘要

In this paper, we give characterizations for distributive, modular, semidistributive, semimodular, 0-distributive and 0-modular lattices using incomparability relations. We generalize these concepts to posets and call them parallel to-distributive, parallel to-modular, parallel to-semidistributive, LU-semimodular, 0-parallel to-distributive and 0-parallel to-modular posets and obtain forbidden configurations for these classes with finite length by means of LU-subposets. (C) 2016 Elsevier B.V. All rights reserved.